Migdal et al, Equation (51)

Time bar (total: 11.6s)

analyze408.0ms (3.5%)

Memory
8.2MiB live, 165.9MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.5s (29.9%)

Memory
-114.2MiB live, 5 255.3MiB allocated
Samples
1.2s5 545×1invalid
1.2s8 256×0valid
144.0ms467×2invalid
54.0ms391×0invalid
32.0ms230×0exit
Precisions
Click to see histograms. Total time spent on operations: 2.0s
ival-pow: 563.0ms (28.5% of total)
ival-mult: 540.0ms (27.3% of total)
ival-div: 326.0ms (16.5% of total)
ival-sqrt: 198.0ms (10% of total)
adjust: 120.0ms (6.1% of total)
ival-sub: 104.0ms (5.3% of total)
ival-pi: 88.0ms (4.5% of total)
exact: 20.0ms (1% of total)
ival-true: 11.0ms (0.6% of total)
ival-assert: 5.0ms (0.3% of total)
Bogosity

preprocess52.0ms (0.5%)

Memory
-11.7MiB live, 71.2MiB allocated
Algorithm
2×egg-herbie
Rules
260×associate-*r*
160×sub-neg
158×associate-*l*
138×distribute-lft-neg-in
124×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033104
18788
220288
339488
462188
589088
6105988
7126488
8132388
9134788
10136588
11136988
12136988
01316
12814
24514
36614
48414
59914
612014
714714
815614
915914
015913
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
Call 2
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))
Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ (pow (* (* 2 (PI)) n) (+ 1/2 (* k -1/2))) (sqrt k))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(/ (pow (* (* 2 (PI)) n) (- 1/2 (* k -1/2))) (sqrt (neg k)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(/ (pow (* n (* (PI) -2)) (+ 1/2 (* k -1/2))) (sqrt k))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(/ (pow (* (* 2 (PI)) n) (- 1/2 (* k -1/2))) (neg (sqrt (neg k))))
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(/ (pow (* n (* (PI) -2)) (+ 1/2 (* k -1/2))) (neg (sqrt k)))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))
(/ (pow (* (PI) (* k 2)) (- 1/2 (* n 1/2))) (sqrt n))

explain172.0ms (1.5%)

Memory
-4.0MiB live, 234.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
299(6.384607195427605e-285 1.203085156885773e+92)0-(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
00-0-k
00-0-n
00-0-(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
00-0-#s(literal 1 binary64)
00-0-(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
00-0-(sqrt.f64 k)
00-0-#s(literal 2 binary64)
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
00-0-(-.f64 #s(literal 1 binary64) k)
00-0-(*.f64 #s(literal 2 binary64) (PI.f64))
00-0-(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
00-0-(PI.f64)
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
pow.f64(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))sensitivity10123
Confusion
Predicted +Predicted -
+20
-99155
Precision
0.019801980198019802
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+200
-9923132
Precision?
0.016129032258064516
Recall?
1.0
Freqs
test
numberfreq
0155
1101
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
71.0ms512×0valid
Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 52.0ms
ival-sub: 21.0ms (40.7% of total)
ival-pow: 9.0ms (17.4% of total)
ival-mult: 8.0ms (15.5% of total)
ival-div: 7.0ms (13.6% of total)
ival-sqrt: 4.0ms (7.7% of total)
ival-pi: 2.0ms (3.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify8.0ms (0.1%)

Memory
11.9MiB live, 11.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01354
12852
24552
36652
48452
59952
612052
714752
815652
915952
015949
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ 1 (sqrt k))
1
(sqrt k)
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (* 2 (PI)) n)
(* 2 (PI))
2
(PI)
n
(/ (- 1 k) 2)
(- 1 k)
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)

localize47.0ms (0.4%)

Memory
-4.7MiB live, 68.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓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))))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Samples
29.0ms256×0valid
Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-pow: 5.0ms (30% of total)
ival-mult: 4.0ms (24% of total)
ival-div: 3.0ms (18% of total)
ival-sqrt: 2.0ms (12% of total)
ival-pi: 1.0ms (6% of total)
ival-sub: 1.0ms (6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series73.0ms (0.6%)

Memory
-6.0MiB live, 109.4MiB allocated
Counts
5 → 84
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 (* (* 2 (PI)) n)>
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 (* 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

21 calls:

TimeVariablePointExpression
36.0ms
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)))
7.0ms
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)))
1.0ms
k
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite296.0ms (2.6%)

Memory
18.4MiB live, 495.3MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 378×*-lowering-*.f32
4 378×*-lowering-*.f64
3 286×pow-lowering-pow.f64
3 286×pow-lowering-pow.f32
2 442×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01338
18035
248833
3445133
0857233
Stop Event
1×iter limit
1×node limit
Counts
5 → 253
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))
(* (* 2 (PI)) n)
Outputs
(exp.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
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(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (*.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)))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.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 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (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 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.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))))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 8 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (-.f64 #s(literal 0 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 #s(literal 1 binary64) k))))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (neg.f64 (/.f64 (*.f64 k (*.f64 k k)) (+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 #s(literal 1 binary64) k)))))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (neg.f64 (/.f64 (*.f64 k k) (+.f64 #s(literal 1 binary64) k)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (-.f64 #s(literal 0 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (PI.f64))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 #s(literal 2 binary64) n))))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 #s(literal 2 binary64) n))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (PI.f64))))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 (PI.f64) n))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 n)))
(*.f64 (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 n)) (pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.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 n (cbrt.f64 (PI.f64))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(*.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)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) n) (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 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 n (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (*.f64 n #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))))
(*.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)))

simplify400.0ms (3.5%)

Memory
0.3MiB live, 620.0MiB allocated
Algorithm
1×egg-herbie
Rules
11 382×accelerator-lowering-fma.f32
11 382×accelerator-lowering-fma.f64
6 430×*-lowering-*.f32
6 430×*-lowering-*.f64
2 486×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01201122
13211103
29541013
33225986
45231908
08739896
Stop Event
1×iter limit
1×node limit
Counts
84 → 84
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)))))
(* 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 (PI.f64) (*.f64 n k))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k)))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) #s(literal -1/48 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) #s(literal 1/8 binary64)))) (*.f64 k k)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k)))) (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 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))
(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))
(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)
(sqrt.f64 k)
(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)))
(sqrt.f64 k)
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 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 (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 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 (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 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 (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 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 (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 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 (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 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 (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 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 (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 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 (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64))))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (+.f64 (*.f64 (*.f64 k #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal -1/2 binary64))))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 k (*.f64 k (*.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 #s(literal 1/8 binary64) (*.f64 (*.f64 k #s(literal -1/48 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)))))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 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 (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 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 (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 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 (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 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 (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 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 (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 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 (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 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 (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 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)))

eval38.0ms (0.3%)

Memory
7.4MiB live, 84.2MiB allocated
Compiler

Compiled 7 188 to 889 computations (87.6% saved)

prune47.0ms (0.4%)

Memory
-7.7MiB live, 111.4MiB allocated
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New32116337
Fresh000
Picked011
Done000
Total32117338
Accuracy
100.0%
Counts
338 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
51.9%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
51.7%
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
99.7%
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
▶99.7%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
51.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
▶99.4%
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶51.3%
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) #s(literal 2 binary64)))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)))
✓99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
52.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
48.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))))
▶42.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
96.0%
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 620 to 447 computations (27.9% saved)

simplify13.0ms (0.1%)

Memory
25.2MiB live, 25.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 k #s(literal 2 binary64))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
✓cost-diff0
(pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓cost-diff0
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
✓cost-diff0
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓cost-diff0
(pow.f64 k #s(literal -1/4 binary64))
✓cost-diff0
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓cost-diff6464
(pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 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)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 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
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓cost-diff0
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
✓cost-diff0
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
Rules
110×*-lowering-*.f32
110×*-lowering-*.f64
56×+-lowering-+.f64
56×+-lowering-+.f32
52×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040286
172280
2100280
3122280
4140280
5155280
6176280
7202280
8214280
9218280
0218277
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ (sqrt (* (PI) (* 2 n))) (* (sqrt k) (pow (* (PI) (* 2 n)) (/ k 2))))
(sqrt (* (PI) (* 2 n)))
(* (PI) (* 2 n))
(PI)
(* 2 n)
2
n
(* (sqrt k) (pow (* (PI) (* 2 n)) (/ k 2)))
(sqrt k)
k
(pow (* (PI) (* 2 n)) (/ k 2))
(/ k 2)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
n
(PI)
k
(sqrt 2)
2
(* (/ 1 (sqrt k)) (/ 1 (pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2)))))
(/ 1 (sqrt k))
1
(sqrt k)
k
(/ 1 (pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2))))
(pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2)))
(* (PI) (* 2 n))
(PI)
(* 2 n)
2
n
(+ -1/2 (/ k 2))
-1/2
(/ k 2)
(* (pow (pow k -1/4) 2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(pow (pow k -1/4) 2)
(pow k -1/4)
k
-1/4
2
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (* 2 (PI)) n)
(* 2 (PI))
(PI)
n
(/ (- 1 k) 2)
(- 1 k)
1
(* (pow 2 (+ 1/2 (/ k 2))) (/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt k)))
(pow 2 (+ 1/2 (/ k 2)))
2
(+ 1/2 (/ k 2))
1/2
(/ k 2)
k
(/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt k))
(pow (* (PI) n) (+ 1/2 (/ k 2)))
(* (PI) n)
(PI)
n
(sqrt k)
Outputs
(/ (sqrt (* (PI) (* 2 n))) (* (sqrt k) (pow (* (PI) (* 2 n)) (/ k 2))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
(sqrt (* (PI) (* 2 n)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(* (PI) (* 2 n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(PI)
(PI.f64)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
2
#s(literal 2 binary64)
n
(* (sqrt k) (pow (* (PI) (* 2 n)) (/ k 2)))
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(sqrt k)
(sqrt.f64 k)
k
(pow (* (PI) (* 2 n)) (/ k 2))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))
(/ k 2)
(/.f64 k #s(literal 2 binary64))
(* (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)
(* (/ 1 (sqrt k)) (/ 1 (pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/ 1 (sqrt k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
1
#s(literal 1 binary64)
(sqrt k)
(sqrt.f64 k)
k
(/ 1 (pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(* (PI) (* 2 n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(PI)
(PI.f64)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
2
#s(literal 2 binary64)
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))
(* (pow (pow k -1/4) 2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(pow (pow k -1/4) 2)
(pow.f64 k #s(literal -1/2 binary64))
(pow k -1/4)
(pow.f64 k #s(literal -1/4 binary64))
k
-1/4
#s(literal -1/4 binary64)
2
#s(literal 2 binary64)
(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 (PI.f64) #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)
1
#s(literal 1 binary64)
(* (pow 2 (+ 1/2 (/ k 2))) (/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt 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 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow 2 (+ 1/2 (/ k 2)))
(pow.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))
2
#s(literal 2 binary64)
(+ 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
(/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt k))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow (* (PI) n) (+ 1/2 (/ k 2)))
(pow.f64 (*.f64 (PI.f64) n) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(sqrt k)
(sqrt.f64 k)

localize175.0ms (1.5%)

Memory
7.3MiB live, 278.5MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(/.f64 (pow.f64 (*.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)
✓accuracy99.3%
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
✓accuracy77.7%
(PI.f64)
✓accuracy99.7%
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓accuracy99.7%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.4%
(pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64))
✓accuracy77.7%
(PI.f64)
✓accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.7%
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓accuracy77.7%
(PI.f64)
✓accuracy99.7%
(*.f64 n (PI.f64))
✓accuracy99.4%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy89.9%
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓accuracy77.7%
(PI.f64)
✓accuracy99.8%
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
✓accuracy99.8%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
✓accuracy99.7%
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓accuracy77.7%
(PI.f64)
Samples
75.0ms197×0valid
19.0ms59×0exit
Compiler

Compiled 288 to 42 computations (85.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 67.0ms
ival-pow: 27.0ms (40.6% of total)
ival-mult: 14.0ms (21% of total)
ival-div: 10.0ms (15% of total)
ival-sqrt: 7.0ms (10.5% of total)
ival-add: 2.0ms (3% of total)
ival-pow2: 2.0ms (3% of total)
ival-pi: 1.0ms (1.5% of total)
ival-sub: 1.0ms (1.5% of total)
exact: 1.0ms (1.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series190.0ms (1.6%)

Memory
-26.4MiB live, 212.7MiB allocated
Counts
23 → 384
Calls
Call 1
Inputs
#<alt (/ (sqrt (* (PI) (* 2 n))) (* (sqrt k) (pow (* (PI) (* 2 n)) (/ k 2))))>
#<alt (sqrt (* (PI) (* 2 n)))>
#<alt (* (PI) (* 2 n))>
#<alt (PI)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (* (/ 1 (sqrt k)) (/ 1 (pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2)))))>
#<alt (/ 1 (sqrt k))>
#<alt (sqrt k)>
#<alt (/ 1 (pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2))))>
#<alt (pow (pow k -1/4) 2)>
#<alt (* (pow (pow k -1/4) 2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))>
#<alt (pow k -1/4)>
#<alt (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))>
#<alt (* (pow 2 (+ 1/2 (/ k 2))) (/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt k)))>
#<alt (pow 2 (+ 1/2 (/ k 2)))>
#<alt (+ 1/2 (/ k 2))>
#<alt (/ k 2)>
#<alt (* (* 2 (PI)) n)>
#<alt (* (PI) n)>
#<alt (/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt k))>
Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))>
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#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (/ (+ (sqrt (* k (* n (PI)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k)>
#<alt (/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2))) (* 1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI)))))))) k)>
#<alt (/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* 1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* 1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))>
Calls

96 calls:

TimeVariablePointExpression
52.0ms
k
@-inf
(pow k -1/4)
42.0ms
n
@0
(* (pow 2 (+ 1/2 (/ k 2))) (/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt k)))
17.0ms
n
@-inf
(* (pow 2 (+ 1/2 (/ k 2))) (/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt k)))
17.0ms
k
@0
(pow k -1/4)
8.0ms
k
@inf
(/ (sqrt (* (PI) (* 2 n))) (* (sqrt k) (pow (* (PI) (* 2 n)) (/ k 2))))

rewrite360.0ms (3.1%)

Memory
27.8MiB live, 619.8MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 374×*-lowering-*.f32
5 374×*-lowering-*.f64
3 476×/-lowering-/.f32
3 476×/-lowering-/.f64
3 040×pow-lowering-pow.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040183
1247158
21672153
08627149
Stop Event
1×iter limit
1×node limit
Counts
23 → 1 087
Calls
Call 1
Inputs
(/ (sqrt (* (PI) (* 2 n))) (* (sqrt k) (pow (* (PI) (* 2 n)) (/ k 2))))
(sqrt (* (PI) (* 2 n)))
(* (PI) (* 2 n))
(PI)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(sqrt (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* n (PI))
(* (/ 1 (sqrt k)) (/ 1 (pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2)))))
(/ 1 (sqrt k))
(sqrt k)
(/ 1 (pow (* (PI) (* 2 n)) (+ -1/2 (/ k 2))))
(pow (pow k -1/4) 2)
(* (pow (pow k -1/4) 2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(pow k -1/4)
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (pow 2 (+ 1/2 (/ k 2))) (/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt k)))
(pow 2 (+ 1/2 (/ k 2)))
(+ 1/2 (/ k 2))
(/ k 2)
(* (* 2 (PI)) n)
(* (PI) n)
(/ (pow (* (PI) n) (+ 1/2 (/ k 2))) (sqrt k))
Outputs
(exp.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/4 binary64) (log.f64 k))) (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/4 binary64) (log.f64 k)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/4 binary64) (log.f64 k))) (*.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/4 binary64) (log.f64 k))) (neg.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))))
(exp.f64 (+.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)) (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)) (*.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)) (neg.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (*.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (neg.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))))
(exp.f64 (+.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))) (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))) (*.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))) (neg.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (log.f64 (pow.f64 k #s(literal -1/2 binary64)))))
(exp.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/4 binary64) (log.f64 k)))))
(exp.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal -1 binary64)) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal -1 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal -1 binary64)) (log.f64 (pow.f64 k #s(literal -1/2 binary64)))))
(exp.f64 (+.f64 (neg.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/4 binary64) (log.f64 k)))))
(exp.f64 (+.f64 (neg.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))) (*.f64 (log.f64 k) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (neg.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (neg.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))) (log.f64 (pow.f64 k #s(literal -1/2 binary64)))))
(exp.f64 (-.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -1/4 binary64) (log.f64 k))) (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))))
(exp.f64 (-.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64)) (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))))
(exp.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))))
(exp.f64 (-.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))))
(exp.f64 (-.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (*.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.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)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (sqrt.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))))
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simplify558.0ms (4.8%)

Memory
20.3MiB live, 729.0MiB allocated
Algorithm
1×egg-herbie
Rules
10 390×accelerator-lowering-fma.f32
10 390×accelerator-lowering-fma.f64
7 992×*-lowering-*.f32
7 992×*-lowering-*.f64
3 596×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04095299
113175010
246554716
084604561
Stop Event
1×iter limit
1×node limit
Counts
384 → 384
Calls
Call 1
Inputs
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(/ (+ (* k (+ (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (* 1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))))))))) (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI)))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI)))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI)))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI)))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n))))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n))))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n))))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n))))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (* k (* (log 2) (sqrt 2)))))
(+ (sqrt 2) (* k (+ (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))) (* 1/2 (* (log 2) (sqrt 2))))))
(+ (sqrt 2) (* k (+ (* 1/2 (* (log 2) (sqrt 2))) (* k (+ (* 1/48 (* k (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2))))))))
(exp (* (log 2) (+ 1/2 (* 1/2 k))))
(exp (* (log 2) (+ 1/2 (* 1/2 k))))
(exp (* (log 2) (+ 1/2 (* 1/2 k))))
(exp (* (log 2) (+ 1/2 (* 1/2 k))))
(exp (* (log 2) (- 1/2 (* -1/2 k))))
(exp (* (log 2) (- 1/2 (* -1/2 k))))
(exp (* (log 2) (- 1/2 (* -1/2 k))))
(exp (* (log 2) (- 1/2 (* -1/2 k))))
1/2
(+ 1/2 (* 1/2 k))
(+ 1/2 (* 1/2 k))
(+ 1/2 (* 1/2 k))
(* 1/2 k)
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(* 1/2 k)
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(* k (+ 1/2 (* 1/2 (/ 1 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)
(* 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))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))
(sqrt (/ (* n (PI)) k))
(/ (+ (sqrt (* k (* n (PI)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2))) (* 1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI)))))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* 1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* 1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))
Outputs
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (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 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k)))) (*.f64 k (+.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) (*.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 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) #s(literal 1/8 binary64)))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k)))) (*.f64 k (+.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) (*.f64 k (-.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 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) #s(literal 1/8 binary64))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) #s(literal -1/8 binary64))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/24 binary64)))))))))) k)
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
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(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))))
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(sqrt 2)
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(exp (* (log 2) (+ 1/2 (* 1/2 k))))
(pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log 2) (+ 1/2 (* 1/2 k))))
(pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log 2) (+ 1/2 (* 1/2 k))))
(pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log 2) (+ 1/2 (* 1/2 k))))
(pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log 2) (- 1/2 (* -1/2 k))))
(pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log 2) (- 1/2 (* -1/2 k))))
(pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log 2) (- 1/2 (* -1/2 k))))
(pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (log 2) (- 1/2 (* -1/2 k))))
(pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 k))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(+ 1/2 (* 1/2 k))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(+ 1/2 (* 1/2 k))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
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(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
(*.f64 k #s(literal 1/2 binary64))
(* 1/2 k)
(*.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))
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(* n (PI))
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(* n (PI))
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(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
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(* n (PI))
(*.f64 n (PI.f64))
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(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (pow.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/ (+ (sqrt (* k (* n (PI)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k)
(/.f64 (+.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (log.f64 (*.f64 n (PI.f64)))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2))) (* 1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI)))))))) k)
(/.f64 (+.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 k (+.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (*.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) #s(literal 1/8 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (log.f64 (*.f64 n (PI.f64)))))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* 1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* 1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k)
(/.f64 (+.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 k (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (log.f64 (*.f64 n (PI.f64))))) (*.f64 k (+.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (*.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 3 binary64)) #s(literal 1/48 binary64))) (*.f64 (pow.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) #s(literal 1/8 binary64)))))))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))
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(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))

eval257.0ms (2.2%)

Memory
-9.6MiB live, 599.4MiB allocated
Compiler

Compiled 41 685 to 3 674 computations (91.2% saved)

prune239.0ms (2.1%)

Memory
-14.5MiB live, 517.4MiB allocated
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New1 896201 916
Fresh11011
Picked505
Done101
Total1 913201 933
Accuracy
100.0%
Counts
1 933 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
99.6%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
42.3%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
78.9%
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
52.4%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
42.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
42.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
42.6%
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
99.6%
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
52.4%
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
79.5%
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
▶42.6%
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
42.5%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
▶42.5%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
▶52.4%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
42.4%
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
52.4%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
39.4%
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
Compiler

Compiled 548 to 428 computations (21.9% saved)

simplify13.0ms (0.1%)

Memory
-10.8MiB live, 28.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 k (*.f64 (PI.f64) n))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
✓cost-diff64
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))
✓cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓cost-diff0
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (/.f64 n k))
✓cost-diff0
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(/.f64 k (*.f64 (PI.f64) n))
✓cost-diff0
(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓cost-diff0
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓cost-diff0
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Rules
120×*-lowering-*.f32
120×*-lowering-*.f64
50×/-lowering-/.f32
50×/-lowering-/.f64
46×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029177
150175
280175
3115175
4138175
5157175
6171175
7187175
8201175
9220175
10223175
0223172
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* (PI) (* 2 n)) (- 1/2 (/ k 2)))
(* (PI) (* 2 n))
(PI)
(* 2 n)
2
n
(- 1/2 (/ k 2))
1/2
(/ k 2)
k
(sqrt k)
(sqrt (/ 2 (/ k (* (PI) n))))
(/ 2 (/ k (* (PI) n)))
2
(/ k (* (PI) n))
k
(* (PI) n)
(PI)
n
(* (sqrt (* (PI) (/ n k))) (sqrt 2))
(sqrt (* (PI) (/ n k)))
(* (PI) (/ n k))
(PI)
(/ n k)
n
k
(sqrt 2)
2
(* (sqrt (* (PI) (* 2 n))) (pow k -1/2))
(sqrt (* (PI) (* 2 n)))
(* (PI) (* 2 n))
(PI)
(* 2 n)
2
n
(pow k -1/2)
k
-1/2
(* (/ 1 (pow (/ k (* (PI) n)) 1/2)) (sqrt 2))
(/ 1 (pow (/ k (* (PI) n)) 1/2))
1
(pow (/ k (* (PI) n)) 1/2)
(/ k (* (PI) n))
k
(* (PI) n)
(PI)
n
1/2
(sqrt 2)
2
Outputs
(/ (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2))) (sqrt k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(pow (* (PI) (* 2 n)) (- 1/2 (/ k 2)))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(* (PI) (* 2 n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(PI)
(PI.f64)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
2
#s(literal 2 binary64)
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)
(sqrt (/ 2 (/ k (* (PI) n))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k (PI.f64))))
(/ 2 (/ k (* (PI) n)))
(/.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k (PI.f64)))
2
#s(literal 2 binary64)
(/ k (* (PI) n))
(/.f64 k (*.f64 (PI.f64) n))
k
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
(* (sqrt (* (PI) (/ n k))) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (* (PI) (/ n k)))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))
(* (PI) (/ n k))
(/.f64 (PI.f64) (/.f64 k n))
(PI)
(PI.f64)
(/ n k)
(/.f64 n k)
n
k
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* (sqrt (* (PI) (* 2 n))) (pow k -1/2))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
(sqrt (* (PI) (* 2 n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
(* (PI) (* 2 n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(PI)
(PI.f64)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
2
#s(literal 2 binary64)
n
(pow k -1/2)
(pow.f64 k #s(literal -1/2 binary64))
k
-1/2
#s(literal -1/2 binary64)
(* (/ 1 (pow (/ k (* (PI) n)) 1/2)) (sqrt 2))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/ 1 (pow (/ k (* (PI) n)) 1/2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
1
#s(literal 1 binary64)
(pow (/ k (* (PI) n)) 1/2)
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
(/ k (* (PI) n))
(/.f64 k (*.f64 (PI.f64) n))
k
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n
1/2
#s(literal 1/2 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)

localize109.0ms (0.9%)

Memory
21.2MiB live, 256.1MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
✓accuracy99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy80.1%
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
✓accuracy99.6%
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓accuracy99.6%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
✓accuracy100.0%
(PI.f64)
✓accuracy99.6%
(*.f64 (PI.f64) (/.f64 n k))
✓accuracy99.3%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy80.1%
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
✓accuracy99.7%
(/.f64 k (*.f64 (PI.f64) n))
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓accuracy79.8%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓accuracy99.8%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓accuracy99.6%
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
Samples
63.0ms256×0valid
Compiler

Compiled 182 to 31 computations (83% saved)

Precisions
Click to see histograms. Total time spent on operations: 44.0ms
ival-div: 11.0ms (25.2% of total)
ival-sqrt: 11.0ms (25.2% of total)
ival-pow: 10.0ms (22.9% of total)
ival-mult: 9.0ms (20.6% of total)
ival-pi: 1.0ms (2.3% of total)
ival-sub: 1.0ms (2.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series21.0ms (0.2%)

Memory
1.6MiB live, 42.4MiB allocated
Counts
16 → 324
Calls
Call 1
Inputs
#<alt (/ (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2))) (sqrt k))>
#<alt (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2)))>
#<alt (* (PI) (* 2 n))>
#<alt (PI)>
#<alt (sqrt (/ 2 (/ k (* (PI) n))))>
#<alt (/ 2 (/ k (* (PI) n)))>
#<alt (/ k (* (PI) n))>
#<alt (* (PI) n)>
#<alt (* (sqrt (* (PI) (/ n k))) (sqrt 2))>
#<alt (sqrt (* (PI) (/ n k)))>
#<alt (* (PI) (/ n k))>
#<alt (* (sqrt (* (PI) (* 2 n))) (pow k -1/2))>
#<alt (sqrt (* (PI) (* 2 n)))>
#<alt (* (/ 1 (pow (/ k (* (PI) n)) 1/2)) (sqrt 2))>
#<alt (pow (/ k (* (PI) n)) 1/2)>
#<alt (/ 1 (pow (/ k (* (PI) n)) 1/2))>
Outputs
#<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 (* (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 (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (* 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 (* (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)) (* (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))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (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 (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (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))>
#<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))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (sqrt (/ (* n (PI)) k)))>
#<alt (* -1 (sqrt (/ (* n (PI)) k)))>
#<alt (* -1 (sqrt (/ (* n (PI)) k)))>
#<alt (* -1 (sqrt (/ (* n (PI)) k)))>
Calls

81 calls:

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

rewrite323.0ms (2.8%)

Memory
-11.7MiB live, 540.5MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 340×*-lowering-*.f32
5 340×*-lowering-*.f64
3 160×/-lowering-/.f32
3 160×/-lowering-/.f64
1 520×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029107
1158107
2976107
08837105
Stop Event
1×iter limit
1×node limit
Counts
16 → 1 016
Calls
Call 1
Inputs
(/ (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* (PI) (* 2 n)) (- 1/2 (/ k 2)))
(* (PI) (* 2 n))
(PI)
(sqrt (/ 2 (/ k (* (PI) n))))
(/ 2 (/ k (* (PI) n)))
(/ k (* (PI) n))
(* (PI) n)
(* (sqrt (* (PI) (/ n k))) (sqrt 2))
(sqrt (* (PI) (/ n k)))
(* (PI) (/ n k))
(* (sqrt (* (PI) (* 2 n))) (pow k -1/2))
(sqrt (* (PI) (* 2 n)))
(* (/ 1 (pow (/ k (* (PI) n)) 1/2)) (sqrt 2))
(pow (/ k (* (PI) n)) 1/2)
(/ 1 (pow (/ k (* (PI) n)) 1/2))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (*.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))))
(exp.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) k) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 k) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (*.f64 (pow.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal -1 binary64))
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(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n))) (pow.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/4 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))))
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) k) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
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(*.f64 (sqrt.f64 n) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))
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(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 k n)) #s(literal 1/2 binary64)))
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(*.f64 (*.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))

simplify511.0ms (4.4%)

Memory
14.4MiB live, 720.5MiB allocated
Algorithm
1×egg-herbie
Rules
10 464×accelerator-lowering-fma.f32
10 464×accelerator-lowering-fma.f64
7 578×*-lowering-*.f32
7 578×*-lowering-*.f64
2 310×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01313046
13572939
210212801
330422774
448132728
087882716
Stop Event
1×iter limit
1×node limit
Counts
324 → 324
Calls
Call 1
Inputs
(* (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)))))
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(* (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)))
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(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(* (sqrt (/ k (* n (PI)))) (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))
(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))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* -1 (sqrt (/ (* n (PI)) k)))
(* -1 (sqrt (/ (* n (PI)) k)))
(* -1 (sqrt (/ (* n (PI)) k)))
(* -1 (sqrt (/ (* n (PI)) k)))
Outputs
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (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 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 (*.f64 (*.f64 k k) (PI.f64)) n))) (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))) 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 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 (*.f64 (*.f64 k k) (PI.f64)) n))) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 k (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) #s(literal 1/8 binary64)) (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 (*.f64 (*.f64 k k) (PI.f64)) n))) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal -1/2 binary64))))))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 k (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))) (+.f64 (*.f64 (*.f64 k #s(literal -1/48 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1/8 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal -1/2 binary64)))))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.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 #s(literal 2 binary64) (PI.f64))) (+.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 #s(literal 2 binary64) (PI.f64))) (+.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 #s(literal 2 binary64) (PI.f64))) (+.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 #s(literal 2 binary64) (PI.f64))) (+.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 #s(literal 2 binary64) (PI.f64))) (+.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 #s(literal 2 binary64) (PI.f64))) (+.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 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* (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) (sqrt -1)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 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))
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(*.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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(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))
(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))
(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)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* -1 (sqrt (/ (* n (PI)) k)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* -1 (sqrt (/ (* n (PI)) k)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* -1 (sqrt (/ (* n (PI)) k)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))

eval320.0ms (2.8%)

Memory
-1.5MiB live, 454.9MiB allocated
Compiler

Compiled 24 913 to 3 196 computations (87.2% saved)

prune216.0ms (1.9%)

Memory
22.1MiB live, 450.1MiB allocated
Pruning

41 alts after pruning (37 fresh and 4 done)

PrunedKeptTotal
New1 665241 689
Fresh21315
Picked145
Done000
Total1 668411 709
Accuracy
100.0%
Counts
1 709 → 41
Alt Table
Click to see full alt table
StatusAccuracyProgram
42.0%
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
42.7%
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
27.2%
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/4 binary64))
52.4%
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
✓99.6%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
99.6%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
42.3%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
78.9%
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
52.4%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
42.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
42.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
42.3%
(*.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
42.6%
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶52.4%
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
52.3%
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))))
▶99.6%
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
79.5%
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
42.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
42.5%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
42.5%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
▶52.4%
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
42.4%
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
✓42.5%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓52.4%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
42.4%
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
52.4%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
42.2%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
42.2%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
✓42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
42.2%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
▶42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)))
42.1%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
42.2%
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
42.2%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
42.1%
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
42.1%
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
▶42.2%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
39.4%
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 997 to 779 computations (21.9% saved)

simplify19.0ms (0.2%)

Memory
-10.9MiB live, 28.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
✓cost-diff0
(/.f64 #s(literal 2 binary64) k)
✓cost-diff0
(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 #s(literal 2 binary64) k)
✓cost-diff0
(*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))
✓cost-diff0
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
✓cost-diff0
(/.f64 k (PI.f64))
✓cost-diff0
(/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n)))
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
✓cost-diff128
(*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))
✓cost-diff0
(/.f64 (PI.f64) k)
✓cost-diff0
(*.f64 #s(literal 2 binary64) n)
✓cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k))
✓cost-diff0
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓cost-diff0
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓cost-diff0
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
Rules
204×*-lowering-*.f32
204×*-lowering-*.f64
140×accelerator-lowering-fma.f32
140×accelerator-lowering-fma.f64
108×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031166
160164
2105164
3163164
4252164
5319164
6338164
7363164
8398164
9457164
10487164
0487161
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2))) (pow k -1/2))
(pow (* (PI) (* 2 n)) (- 1/2 (/ k 2)))
(* (PI) (* 2 n))
(PI)
(* 2 n)
2
n
(- 1/2 (/ k 2))
1/2
(/ k 2)
k
(pow k -1/2)
-1/2
(sqrt (* (* 2 n) (/ (PI) k)))
(* (* 2 n) (/ (PI) k))
(* 2 n)
2
n
(/ (PI) k)
(PI)
k
(sqrt (/ 2 (* (/ k (PI)) (/ 1 n))))
(/ 2 (* (/ k (PI)) (/ 1 n)))
2
(* (/ k (PI)) (/ 1 n))
(/ k (PI))
k
(PI)
(/ 1 n)
1
n
(* (sqrt (* (/ 2 k) (PI))) (sqrt n))
(sqrt (* (/ 2 k) (PI)))
(* (/ 2 k) (PI))
(/ 2 k)
2
k
(PI)
(sqrt n)
n
(* (pow (/ 2 k) 1/2) (pow (* (PI) n) 1/2))
(pow (/ 2 k) 1/2)
(/ 2 k)
2
k
1/2
(pow (* (PI) n) 1/2)
(* (PI) n)
(PI)
n
Outputs
(* (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2))) (pow k -1/2))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(pow (* (PI) (* 2 n)) (- 1/2 (/ k 2)))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(* (PI) (* 2 n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(PI)
(PI.f64)
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
2
#s(literal 2 binary64)
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
(pow k -1/2)
(pow.f64 k #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(sqrt (* (* 2 n) (/ (PI) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(* (* 2 n) (/ (PI) k))
(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))
(* 2 n)
(*.f64 #s(literal 2 binary64) n)
2
#s(literal 2 binary64)
n
(/ (PI) k)
(/.f64 (PI.f64) k)
(PI)
(PI.f64)
k
(sqrt (/ 2 (* (/ k (PI)) (/ 1 n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(/ 2 (* (/ k (PI)) (/ 1 n)))
(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))
2
#s(literal 2 binary64)
(* (/ k (PI)) (/ 1 n))
(/.f64 (/.f64 k (PI.f64)) n)
(/ k (PI))
(/.f64 k (PI.f64))
k
(PI)
(PI.f64)
(/ 1 n)
(/.f64 #s(literal 1 binary64) n)
1
#s(literal 1 binary64)
n
(* (sqrt (* (/ 2 k) (PI))) (sqrt n))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (sqrt.f64 n))
(sqrt (* (/ 2 k) (PI)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))
(* (/ 2 k) (PI))
(/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
2
#s(literal 2 binary64)
k
(PI)
(PI.f64)
(sqrt n)
(sqrt.f64 n)
n
(* (pow (/ 2 k) 1/2) (pow (* (PI) n) 1/2))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(pow (/ 2 k) 1/2)
(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64))
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
2
#s(literal 2 binary64)
k
1/2
#s(literal 1/2 binary64)
(pow (* (PI) n) 1/2)
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
(* (PI) n)
(*.f64 (PI.f64) n)
(PI)
(PI.f64)
n

localize117.0ms (1%)

Memory
-36.2MiB live, 257.8MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.8%
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
✓accuracy99.8%
(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64))
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.5%
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
✓accuracy99.6%
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
✓accuracy99.4%
(*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))
✓accuracy99.7%
(/.f64 k (PI.f64))
✓accuracy99.6%
(*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))
✓accuracy99.6%
(/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n)))
✓accuracy79.8%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
✓accuracy100.0%
(PI.f64)
✓accuracy99.7%
(*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k))
✓accuracy99.6%
(/.f64 (PI.f64) k)
✓accuracy79.8%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓accuracy99.7%
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
✓accuracy99.6%
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
Samples
64.0ms256×0valid
Compiler

Compiled 176 to 33 computations (81.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 44.0ms
ival-mult: 12.0ms (27.2% of total)
ival-pow: 10.0ms (22.6% of total)
ival-div: 9.0ms (20.4% of total)
ival-sqrt: 9.0ms (20.4% of total)
ival-sub: 3.0ms (6.8% of total)
ival-pi: 1.0ms (2.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory
37.1MiB live, 37.1MiB allocated
Counts
20 → 336
Calls
Call 1
Inputs
#<alt (* (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2))) (pow k -1/2))>
#<alt (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2)))>
#<alt (* (PI) (* 2 n))>
#<alt (PI)>
#<alt (sqrt (* (* 2 n) (/ (PI) k)))>
#<alt (* (* 2 n) (/ (PI) k))>
#<alt (* 2 n)>
#<alt (/ (PI) k)>
#<alt (* (/ k (PI)) (/ 1 n))>
#<alt (sqrt (/ 2 (* (/ k (PI)) (/ 1 n))))>
#<alt (/ 2 (* (/ k (PI)) (/ 1 n)))>
#<alt (/ k (PI))>
#<alt (* (sqrt (* (/ 2 k) (PI))) (sqrt n))>
#<alt (sqrt (* (/ 2 k) (PI)))>
#<alt (* (/ 2 k) (PI))>
#<alt (/ 2 k)>
#<alt (* (pow (/ 2 k) 1/2) (pow (* (PI) n) 1/2))>
#<alt (pow (/ 2 k) 1/2)>
#<alt (pow (* (PI) n) 1/2)>
#<alt (* (PI) n)>
Outputs
#<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)))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (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 (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (PI))>
#<alt (/ k (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 (* (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)) (* (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 (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (* 2 (/ (PI) k))>
#<alt (/ 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 (* (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)) (* (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 (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* 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))>
Calls

84 calls:

TimeVariablePointExpression
1.0ms
k
@-inf
(* (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2))) (pow k -1/2))
1.0ms
n
@-inf
(pow (* (PI) n) 1/2)
0.0ms
k
@0
(sqrt (* (/ 2 k) (PI)))
0.0ms
n
@inf
(pow (* (PI) n) 1/2)
0.0ms
k
@-inf
(sqrt (* (/ 2 k) (PI)))

rewrite334.0ms (2.9%)

Memory
15.4MiB live, 712.4MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 622×*-lowering-*.f32
4 622×*-lowering-*.f64
3 920×/-lowering-/.f32
3 920×/-lowering-/.f64
1 646×frac-times
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031117
1173117
21156117
08387115
Stop Event
1×iter limit
1×node limit
Counts
20 → 1 235
Calls
Call 1
Inputs
(* (pow (* (PI) (* 2 n)) (- 1/2 (/ k 2))) (pow k -1/2))
(pow (* (PI) (* 2 n)) (- 1/2 (/ k 2)))
(* (PI) (* 2 n))
(PI)
(sqrt (* (* 2 n) (/ (PI) k)))
(* (* 2 n) (/ (PI) k))
(* 2 n)
(/ (PI) k)
(* (/ k (PI)) (/ 1 n))
(sqrt (/ 2 (* (/ k (PI)) (/ 1 n))))
(/ 2 (* (/ k (PI)) (/ 1 n)))
(/ k (PI))
(* (sqrt (* (/ 2 k) (PI))) (sqrt n))
(sqrt (* (/ 2 k) (PI)))
(* (/ 2 k) (PI))
(/ 2 k)
(* (pow (/ 2 k) 1/2) (pow (* (PI) n) 1/2))
(pow (/ 2 k) 1/2)
(pow (* (PI) n) 1/2)
(* (PI) n)
Outputs
(exp.f64 (+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (*.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (neg.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (/.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal -2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal -2 binary64))))
(*.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (PI.f64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 n (/.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) k)))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) k)))))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) k)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) k)))))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (/.f64 k #s(literal 2 binary64)))))
(exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))))
(exp.f64 (*.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal 2 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (log.f64 (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(exp.f64 (+.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))))
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 1/2 binary64)) (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 k #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (/.f64 (*.f64 k (*.f64 k k)) #s(literal 8 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 k #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 (/.f64 (*.f64 k k) (+.f64 k #s(literal 1 binary64))) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 k (*.f64 k k)) #s(literal -8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 k #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
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(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) n)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 #s(literal 2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) k)) #s(literal 1/4 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k)))
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(pow.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
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(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
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(*.f64 (exp.f64 (log.f64 n)) (PI.f64))

simplify556.0ms (4.8%)

Memory
-7.5MiB live, 827.0MiB allocated
Algorithm
1×egg-herbie
Rules
9 438×accelerator-lowering-fma.f32
9 438×accelerator-lowering-fma.f64
7 232×*-lowering-*.f32
7 232×*-lowering-*.f64
1 712×neg-lowering-neg.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01352930
13602907
210272777
330082750
450312710
085732698
Stop Event
1×iter limit
1×node limit
Counts
336 → 336
Calls
Call 1
Inputs
(* (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)))))
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(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))))
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(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))))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (sqrt 2))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(* 2 (/ (PI) k))
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
Outputs
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
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(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))
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(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))
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(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (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 k (*.f64 n (PI.f64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 k (*.f64 n (PI.f64)))))) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 k (*.f64 n (PI.f64)))))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (*.f64 k (*.f64 (*.f64 k (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) #s(literal 1/8 binary64)) (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 k (*.f64 n (PI.f64)))))) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
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(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
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(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 (*.f64 (*.f64 k #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1/2 binary64))))))
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(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
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(* 2 (* n (PI)))
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(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (PI) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(* (sqrt (/ (PI) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(* (sqrt (/ (PI) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(* (sqrt (/ (PI) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(* (sqrt (/ (PI) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(* (sqrt (/ (PI) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(* (sqrt (/ (PI) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(* (sqrt (/ (PI) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
(* (sqrt (/ (PI) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))))
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(* 2 (/ (PI) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) k)
(/ 2 k)
(/.f64 #s(literal 2 binary64) 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) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 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)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 #s(literal -1 binary64))))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.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))
(* n (PI))
(*.f64 n (PI.f64))

eval255.0ms (2.2%)

Memory
12.1MiB live, 497.6MiB allocated
Compiler

Compiled 24 773 to 3 644 computations (85.3% saved)

prune261.0ms (2.3%)

Memory
-35.0MiB live, 449.9MiB allocated
Pruning

54 alts after pruning (46 fresh and 8 done)

PrunedKeptTotal
New1 785221 807
Fresh82432
Picked145
Done044
Total1 794541 848
Accuracy
100.0%
Counts
1 848 → 54
Alt Table
Click to see full alt table
StatusAccuracyProgram
42.0%
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
42.7%
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
18.8%
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
27.1%
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/4 binary64))
52.4%
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 n #s(literal -1/2 binary64)))
52.4%
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
✓99.6%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
52.4%
(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))
99.6%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
42.3%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
78.9%
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
52.4%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
42.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
42.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
42.6%
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
42.1%
(*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
42.3%
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
52.3%
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))))
52.4%
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
✓99.6%
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
52.4%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
79.5%
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
42.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
52.4%
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
42.5%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
42.5%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓52.4%
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
42.4%
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
✓42.5%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓52.4%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
42.3%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
42.1%
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (/.f64 #s(literal 1 binary64) (PI.f64))))
42.1%
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
42.2%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
42.2%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
42.2%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
✓42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
42.2%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) n))))
42.2%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
✓42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))
42.1%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)))
42.1%
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))))
42.2%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
42.1%
(sqrt.f64 (*.f64 (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) k)))
42.2%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
42.1%
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
42.1%
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
✓42.2%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
39.4%
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))
Compiler

Compiled 1 707 to 818 computations (52.1% saved)

regimes115.0ms (1%)

Memory
41.2MiB live, 196.2MiB allocated
Counts
83 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 n #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal -2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
Outputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
Calls

4 calls:

34.0ms
(*.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))))
26.0ms
n
24.0ms
k
23.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
99.7%1k
99.7%1n
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes149.0ms (1.3%)

Memory
-22.3MiB live, 172.7MiB allocated
Counts
78 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 n #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(*.f64 (exp.f64 (*.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/4 binary64) (/.f64 k #s(literal 4 binary64)))) #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
Outputs
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Calls

4 calls:

48.0ms
k
47.0ms
n
24.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms
(*.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)

regimes49.0ms (0.4%)

Memory
-3.8MiB live, 83.3MiB allocated
Counts
61 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 n #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Outputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
(*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
Calls

2 calls:

25.0ms
k
19.0ms
n
Results
AccuracySegmentsBranch
66.7%2k
56.4%2n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes22.0ms (0.2%)

Memory
2.4MiB live, 41.4MiB allocated
Counts
59 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 n #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))))
Outputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
Calls

1 calls:

18.0ms
k
Results
AccuracySegmentsBranch
59.0%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory
-6.1MiB live, 32.1MiB allocated
Counts
38 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
Calls

1 calls:

12.0ms
k
Results
AccuracySegmentsBranch
59.0%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes21.0ms (0.2%)

Memory
5.8MiB live, 43.6MiB allocated
Counts
28 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) n))))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) #s(literal 1/4 binary64))
Outputs
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64))
Calls

2 calls:

10.0ms
n
8.0ms
k
Results
AccuracySegmentsBranch
42.7%1n
49.3%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes20.0ms (0.2%)

Memory
-2.1MiB live, 40.0MiB allocated
Counts
25 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) n))))
Outputs
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
Calls

2 calls:

11.0ms
n
8.0ms
k
Results
AccuracySegmentsBranch
42.7%1n
42.7%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory
25.0MiB live, 25.0MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64)) (/.f64 n k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
Outputs
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
Calls

2 calls:

4.0ms
n
3.0ms
k
Results
AccuracySegmentsBranch
42.2%1k
42.2%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Memory
-21.4MiB live, 17.7MiB allocated
Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

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

2 calls:

3.0ms
n
2.0ms
k
Results
AccuracySegmentsBranch
42.2%1k
42.2%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch18.0ms (0.2%)

Memory
4.9MiB live, 44.2MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
16.0ms
1.2527655510165586e-17
7.303153925885367e-15
Samples
12.0ms128×0valid
Compiler

Compiled 245 to 202 computations (17.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-div: 2.0ms (23% of total)
ival-mult: 2.0ms (23% of total)
ival-pow: 2.0ms (23% of total)
ival-sub: 1.0ms (11.5% of total)
ival-sqrt: 1.0ms (11.5% of total)
ival-pi: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

bsearch14.0ms (0.1%)

Memory
-15.8MiB live, 23.2MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
10.0ms
4.663813160078993e+179
1.241701571877239e+180
Samples
7.0ms80×0valid
Compiler

Compiled 171 to 128 computations (25.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-div: 1.0ms (19.5% of total)
ival-mult: 1.0ms (19.5% of total)
ival-sqrt: 1.0ms (19.5% of total)
ival-pow: 1.0ms (19.5% of total)
ival-pi: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

bsearch11.0ms (0.1%)

Memory
21.8MiB live, 21.8MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
10.0ms
4.663813160078993e+179
1.241701571877239e+180
Samples
7.0ms80×0valid
Compiler

Compiled 171 to 128 computations (25.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-div: 1.0ms (19.7% of total)
ival-mult: 1.0ms (19.7% of total)
ival-sqrt: 1.0ms (19.7% of total)
ival-pow: 1.0ms (19.7% of total)
ival-pi: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

bsearch11.0ms (0.1%)

Memory
12.7MiB live, 12.7MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
10.0ms
4.663813160078993e+179
1.241701571877239e+180
Samples
7.0ms80×0valid
Compiler

Compiled 171 to 128 computations (25.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-div: 1.0ms (20.6% of total)
ival-mult: 1.0ms (20.6% of total)
ival-sqrt: 1.0ms (20.6% of total)
ival-pow: 1.0ms (20.6% of total)
ival-pi: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

simplify38.0ms (0.3%)

Memory
-28.7MiB live, 11.1MiB allocated
Algorithm
1×egg-herbie
Rules
28×*-commutative_binary64
8×+-commutative_binary64
8×sub-neg_binary64
6×neg-sub0_binary64
6×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050168
163168
272168
378168
483168
585168
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 7098843361278085/40564819207303340847894502572032 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)) (*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
(if (<=.f64 k #s(literal 470000000000000006650260492155167816945114576514269621217819977228282373830402496152234648365777826675307313496032383758295591344885219982298353782170642035741333908365021129211904 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 470000000000000006650260492155167816945114576514269621217819977228282373830402496152234648365777826675307313496032383758295591344885219982298353782170642035741333908365021129211904 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 470000000000000006650260492155167816945114576514269621217819977228282373830402496152234648365777826675307313496032383758295591344885219982298353782170642035741333908365021129211904 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
Outputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 7098843361278085/40564819207303340847894502572032 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)) (*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
(if (<=.f64 k #s(literal 470000000000000006650260492155167816945114576514269621217819977228282373830402496152234648365777826675307313496032383758295591344885219982298353782170642035741333908365021129211904 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 470000000000000006650260492155167816945114576514269621217819977228282373830402496152234648365777826675307313496032383758295591344885219982298353782170642035741333908365021129211904 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 470000000000000006650260492155167816945114576514269621217819977228282373830402496152234648365777826675307313496032383758295591344885219982298353782170642035741333908365021129211904 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 470000000000000006650260492155167816945114576514269621217819977228282373830402496152234648365777826675307313496032383758295591344885219982298353782170642035741333908365021129211904 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))

soundness1.0s (9.1%)

Memory
55.6MiB live, 790.9MiB allocated
Rules
11 382×accelerator-lowering-fma.f32
11 382×accelerator-lowering-fma.f64
6 430×*-lowering-*.f32
6 430×*-lowering-*.f64
5 374×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01201122
13211103
29541013
33225986
45231908
08739896
031117
1173117
21156117
08387115
029107
1158107
2976107
08837105
040183
1247158
21672153
08627149
01338
18035
248833
3445133
0857233
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 516 to 332 computations (35.7% saved)

preprocess152.0ms (1.3%)

Memory
-14.8MiB live, 138.2MiB allocated
Compiler

Compiled 376 to 126 computations (66.5% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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