Migdal et al, Equation (51)

Time bar (total: 11.8s)

analyze169.0ms (1.4%)

Memory
0.2MiB live, 154.5MiB 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)

sample4.3s (36.4%)

Memory
-76.0MiB live, 4 780.8MiB allocated
Samples
1.6s8 256×0valid
1.1s3 520×1invalid
504.0ms1 830×1exit
210.0ms448×2invalid
41.0ms475×0invalid
30.0ms247×0exit
Precisions
Click to see histograms. Total time spent on operations: 2.7s
ival-mult: 904.0ms (33.5% of total)
ival-pow: 617.0ms (22.9% of total)
ival-sqrt: 365.0ms (13.5% of total)
adjust: 274.0ms (10.2% of total)
ival-div: 264.0ms (9.8% of total)
ival-sub: 146.0ms (5.4% of total)
ival-pi: 98.0ms (3.6% of total)
exact: 15.0ms (0.6% of total)
ival-true: 12.0ms (0.4% of total)
ival-assert: 6.0ms (0.2% of total)
Bogosity

preprocess54.0ms (0.5%)

Memory
5.0MiB live, 43.6MiB allocated
Algorithm
1×egg-herbie
Rules
232×associate-*r*
160×sub-neg
160×associate-*l*
138×distribute-lft-neg-in
118×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03188
18274
219374
338374
460774
587874
6104774
7123074
8128574
9130974
10132774
11133174
12133174
01316
02216
13714
25414
37514
49314
510814
612914
715614
816514
916814
016813
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))

explain155.0ms (1.3%)

Memory
0.7MiB live, 287.9MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
489(2.6089265558196728e-42 2.4587946235778597e+178)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)))sensitivity9323
Confusion
Predicted +Predicted -
+50
-88163
Precision
0.053763440860215055
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+500
-8823140
Precision?
0.04310344827586207
Recall?
1.0
Freqs
test
numberfreq
0163
193
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
60.0ms512×0valid
Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 41.0ms
ival-pow: 12.0ms (29.3% of total)
ival-mult: 10.0ms (24.4% of total)
ival-div: 8.0ms (19.5% of total)
ival-sqrt: 4.0ms (9.8% of total)
ival-pi: 3.0ms (7.3% of total)
ival-sub: 3.0ms (7.3% of total)
exact: 1.0ms (2.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.4MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify11.0ms (0.1%)

Memory
-23.6MiB live, 15.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff320
(*.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))))
✓cost-diff512
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
Rules
64×lower-*.f32
58×lower-*.f64
48×lower-+.f64
48×lower-+.f32
36×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01354
02254
13752
25452
37552
49352
510852
612952
715652
816552
916852
016849
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)

localize44.0ms (0.4%)

Memory
0.5MiB live, 81.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓accuracy99.7%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓accuracy99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
Samples
27.0ms256×0valid
Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-pow: 5.0ms (27.9% of total)
ival-mult: 4.0ms (22.3% of total)
ival-div: 3.0ms (16.7% of total)
ival-sqrt: 3.0ms (16.7% of total)
ival-pi: 1.0ms (5.6% of total)
ival-sub: 1.0ms (5.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series68.0ms (0.6%)

Memory
32.4MiB live, 107.6MiB allocated
Counts
6 → 96
Calls
Call 1
Inputs
#<alt (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))>
#<alt (*.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))))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))>
#<alt (sqrt.f64 k)>
#<alt (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)>
#<alt (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))>
Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/2 k))>
#<alt (+ 1/2 (* -1/2 k))>
#<alt (+ 1/2 (* -1/2 k))>
#<alt (* -1/2 k)>
#<alt (* k (- (* 1/2 (/ 1 k)) 1/2))>
#<alt (* k (- (* 1/2 (/ 1 k)) 1/2))>
#<alt (* k (- (* 1/2 (/ 1 k)) 1/2))>
#<alt (* -1/2 k)>
#<alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))>
#<alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))>
#<alt (* -1 (* k (- 1/2 (* 1/2 (/ 1 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 (* 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 (* 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 (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)))))>
Calls

24 calls:

TimeVariablePointExpression
30.0ms
n
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
20.0ms
n
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
9.0ms
n
@inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms
k
@-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)))

rewrite272.0ms (2.3%)

Memory
10.4MiB live, 362.3MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 378×lower-*.f32
4 372×lower-*.f64
3 286×lower-pow.f32
3 284×lower-pow.f64
2 442×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01343
02243
18940
249738
3447438
0859937
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
6 → 419
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
Outputs
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) (*.f64 k #s(literal -1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (neg.f64 k)))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(+.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(+.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 k)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(-.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 k #s(literal 1/4 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 k k (+.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (/.f64 (/.f64 (*.f64 k (*.f64 k k)) (fma.f64 k k (+.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
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(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (PI.f64))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) n))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) n))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (PI.f64))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 (PI.f64) n))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 n)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 n)) (pow.f64 (exp.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))

simplify291.0ms (2.5%)

Memory
-13.9MiB live, 579.5MiB allocated
Algorithm
1×egg-herbie
Rules
9 974×lower-fma.f64
9 974×lower-fma.f32
5 988×lower-*.f64
5 988×lower-*.f32
1 688×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01281174
13451155
210111065
333481038
45547966
08354945
Stop Event
1×iter limit
1×node limit
Counts
96 → 96
Calls
Call 1
Inputs
1/2
(+ 1/2 (* -1/2 k))
(+ 1/2 (* -1/2 k))
(+ 1/2 (* -1/2 k))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* -1/2 k)
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* 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)))
(* 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)))
(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)))))
Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 k))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 k))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 k))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* -1/2 k)
(*.f64 #s(literal -1/2 binary64) k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* k (- (* 1/2 (/ 1 k)) 1/2))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* -1/2 k)
(*.f64 #s(literal -1/2 binary64) k)
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(fma.f64 #s(literal -1/2 binary64) 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)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 (PI.f64) (*.f64 k n))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 (PI.f64) (*.f64 k n))))) #s(literal 1/8 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.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))) (fma.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 (PI.f64) (*.f64 k n))))) #s(literal -1/48 binary64)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))) #s(literal 1/8 binary64)))) (*.f64 k k))) 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))) (fma.f64 #s(literal -1/2 binary64) 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))) (fma.f64 #s(literal -1/2 binary64) 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))) (fma.f64 #s(literal -1/2 binary64) 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))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(* (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))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(* (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))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(* (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))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(* (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))) (fma.f64 #s(literal -1/2 binary64) 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))) (fma.f64 #s(literal -1/2 binary64) 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))) (fma.f64 #s(literal -1/2 binary64) 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))) (fma.f64 #s(literal -1/2 binary64) 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))) (fma.f64 #s(literal -1/2 binary64) 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)) (fma.f64 #s(literal -1/2 binary64) 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)) (fma.f64 #s(literal -1/2 binary64) 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)) (fma.f64 #s(literal -1/2 binary64) 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)) (fma.f64 #s(literal -1/2 binary64) 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)
(* 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)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 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)) (fma.f64 #s(literal -1/2 binary64) 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)) (fma.f64 #s(literal -1/2 binary64) 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)) (fma.f64 #s(literal -1/2 binary64) 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)) (fma.f64 #s(literal -1/2 binary64) 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 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (fma.f64 (*.f64 k #s(literal 1/8 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 k (*.f64 (*.f64 k (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (fma.f64 (*.f64 k #s(literal -1/48 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) k) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))

eval72.0ms (0.6%)

Memory
27.9MiB live, 174.0MiB allocated
Compiler

Compiled 11 242 to 1 530 computations (86.4% saved)

prune77.0ms (0.7%)

Memory
7.2MiB live, 207.1MiB allocated
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New49520515
Fresh000
Picked101
Done000
Total49620516
Accuracy
100.0%
Counts
516 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
99.7%
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
50.9%
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 (PI.f64) (*.f64 k n))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))))) k)
▶99.7%
(/.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 1/2 binary64)))))
99.5%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
45.9%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
46.1%
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
▶55.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
47.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))
▶23.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))))
▶99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
47.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
▶37.9%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
99.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
Compiler

Compiled 780 to 556 computations (28.7% saved)

simplify23.0ms (0.2%)

Memory
-30.0MiB live, 50.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff704
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff128
(-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
✓cost-diff704
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
✓cost-diff0
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff320
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
✓cost-diff0
(*.f64 n (PI.f64))
✓cost-diff0
(/.f64 (*.f64 n (PI.f64)) k)
✓cost-diff0
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓cost-diff0
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
Rules
270×lower-*.f32
240×lower-*.f64
92×*-commutative
80×associate-*r*
68×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040302
072302
1116296
2191296
3264296
4289296
5309296
6335296
7359296
8372296
9378296
10386296
11391296
0391292
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(/.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 1/2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(sqrt.f64 k)
k
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (PI.f64))
n
(PI.f64)
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.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 -1/2 binary64))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
#s(literal -1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))))
(pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))
(*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))
#s(literal 4 binary64)
(*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))
(+.f64 #s(literal 1 binary64) k)
#s(literal -4 binary64)
Outputs
(/.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 1/2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(sqrt.f64 k)
k
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
n
(PI.f64)
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #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 -1/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 n #s(literal 4 binary64))))) (+.f64 (/.f64 k #s(literal -4 binary64)) #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 n #s(literal 4 binary64))))) (+.f64 (/.f64 k #s(literal -4 binary64)) #s(literal -1/4 binary64))))
(pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))
(pow.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 n #s(literal 4 binary64))))) (+.f64 (/.f64 k #s(literal -4 binary64)) #s(literal -1/4 binary64)))
(*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))
(*.f64 n (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 n #s(literal 4 binary64)))))
#s(literal 4 binary64)
(*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 n n)))
(*.f64 (PI.f64) n)
(PI.f64)
n
(/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))
(+.f64 (/.f64 k #s(literal -4 binary64)) #s(literal -1/4 binary64))
(+.f64 #s(literal 1 binary64) k)
(+.f64 k #s(literal 1 binary64))
#s(literal -4 binary64)

localize161.0ms (1.4%)

Memory
-19.2MiB live, 359.8MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))))
✓accuracy75.5%
(pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))
✓accuracy49.7%
(PI.f64)
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
✓accuracy99.7%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
✓accuracy49.7%
(PI.f64)
✓accuracy100.0%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
✓accuracy99.8%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy49.7%
(PI.f64)
✓accuracy99.8%
(*.f64 n (PI.f64))
✓accuracy99.7%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy90.7%
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓accuracy49.7%
(PI.f64)
✓accuracy99.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓accuracy99.8%
(*.f64 (PI.f64) n)
✓accuracy99.7%
(/.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 1/2 binary64)))))
✓accuracy49.7%
(PI.f64)
Samples
56.0ms133×0exit
39.0ms123×0valid
Compiler

Compiled 304 to 42 computations (86.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 68.0ms
ival-mult: 31.0ms (45.4% of total)
ival-pow: 16.0ms (23.4% of total)
ival-div: 9.0ms (13.2% of total)
ival-sqrt: 7.0ms (10.3% of total)
ival-sub: 2.0ms (2.9% of total)
ival-pi: 1.0ms (1.5% of total)
ival-add: 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)

series126.0ms (1.1%)

Memory
6.2MiB live, 161.8MiB allocated
Counts
20 → 360
Calls
Call 1
Inputs
#<alt (/.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 1/2 binary64)))))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
#<alt (*.f64 (PI.f64) n)>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))>
#<alt (sqrt.f64 k)>
#<alt (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))>
#<alt (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))))>
#<alt (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))))>
#<alt (PI.f64)>
#<alt (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))>
#<alt (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))>
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 (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (* n (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 (/ 1 k))>
#<alt (/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k)>
#<alt (/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k)>
#<alt (/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
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#<alt (+ (* k (+ (* -1/4 (* (pow 1/4 1/4) (* (sqrt (/ 1 (* n (PI)))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* k (+ (* -1/384 (* (pow 1/4 1/4) (* (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3)) (sqrt (/ 1 (* n (PI))))))) (* 1/32 (* (pow 1/4 1/4) (* (sqrt (/ 1 (* n (PI)))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))))) (* (pow 1/4 1/4) (sqrt (/ 1 (* n (PI))))))>
#<alt (exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1 k))))>
#<alt (exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1 k))))>
#<alt (exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1 k))))>
#<alt (exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1 k))))>
#<alt (exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))>
#<alt (exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))>
#<alt (exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))>
#<alt (exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))>
Calls

90 calls:

TimeVariablePointExpression
73.0ms
n
@0
(* (/ 1 (sqrt k)) (/ 1 (pow (* 4 (* (* (PI) n) (* (PI) n))) (/ (+ 1 k) -4))))
8.0ms
n
@inf
(* (/ 1 (sqrt k)) (/ 1 (pow (* 4 (* (* (PI) n) (* (PI) n))) (/ (+ 1 k) -4))))
2.0ms
k
@-inf
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
2.0ms
k
@0
(* (/ 1 (sqrt k)) (/ 1 (pow (* 4 (* (* (PI) n) (* (PI) n))) (/ (+ 1 k) -4))))
2.0ms
n
@0
(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))

rewrite297.0ms (2.5%)

Memory
32.8MiB live, 507.7MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 428×lower-*.f32
4 398×lower-*.f64
2 874×lower-pow.f32
2 866×lower-pow.f64
2 748×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040179
072169
1269160
21583153
08282151
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
20 → 926
Calls
Call 1
Inputs
(/.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 1/2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (PI.f64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))))
(PI.f64)
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))
Outputs
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(exp.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64) (*.f64 (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64) (neg.f64 (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))))
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64)) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (*.f64 (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 k)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 (-.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (sqrt.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 k)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 (-.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64))))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 (-.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64)))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64)))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/4 binary64))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (neg.f64 (*.f64 (PI.f64) n)))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (neg.f64 k))))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 1/2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 (-.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64)))))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/4 binary64) (*.f64 k #s(literal -1/4 binary64))))))
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(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 4 binary64)) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (PI.f64)) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 (*.f64 (*.f64 n n) #s(literal 4 binary64)) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) n)) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 (*.f64 n #s(literal 4 binary64)) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 4 binary64) (PI.f64)) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) n)) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (PI.f64) (PI.f64))) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 (*.f64 n n) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
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(*.f64 (pow.f64 (*.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 4 binary64)) (PI.f64)) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 n (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
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(*.f64 (pow.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 (*.f64 (*.f64 n (*.f64 (PI.f64) n)) #s(literal 4 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
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(*.f64 (pow.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (PI.f64) n))) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 (PI.f64) n))) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 (*.f64 (*.f64 n n) #s(literal 4 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
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(*.f64 (pow.f64 (*.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))) (pow.f64 (*.f64 n (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal -1/8 binary64)))))
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simplify424.0ms (3.6%)

Memory
-7.9MiB live, 706.2MiB allocated
Algorithm
1×egg-herbie
Rules
8 506×lower-fma.f64
8 506×lower-fma.f32
8 436×lower-*.f64
8 436×lower-*.f32
2 680×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04065392
112845172
247865053
091144886
Stop Event
1×iter limit
1×node limit
Counts
360 → 360
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
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(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
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(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (sqrt 2))
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(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
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(* (sqrt (* n (PI))) (sqrt 2))
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(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
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(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))
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(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))
(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 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))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.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))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.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))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.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))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.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))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.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))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.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))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.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))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.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))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(* -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))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(* -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))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(* -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))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(* (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 (fma.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 (PI.f64) (*.f64 n 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 (fma.f64 k (fma.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))))) (*.f64 (sqrt.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 (* (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 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) (*.f64 (neg.f64 k) (fma.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (fma.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)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/8 binary64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n k))))) 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 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(* 2 (* n (PI)))
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(* 2 (* n (PI)))
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(* 2 (* n (PI)))
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(* 2 (* n (PI)))
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(* 2 (* n (PI)))
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(* 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))
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(* n (PI))
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(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (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)))
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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)))
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(*.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))))
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(* -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 (/ (* 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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(* (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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(* (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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(sqrt (/ (* n (PI)) k))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
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(sqrt (/ (* n (PI)) k))
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(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
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(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(fma.f64 k (*.f64 k (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/8 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64)) (*.f64 k (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) #s(literal 1/48 binary64)))) (*.f64 k k)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))
(exp.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))
(exp.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))
(exp.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))
(exp.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))
(exp.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))
(exp.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))
(exp.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))
(exp.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (log.f64 n) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))))))
(exp.f64 (*.f64 (fma.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))))))
(exp.f64 (*.f64 (fma.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))))))
(exp.f64 (*.f64 (fma.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(exp (* -1/4 (* (+ 1 k) (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))))))
(exp.f64 (*.f64 (fma.f64 #s(literal -2 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)) (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 4 binary64))))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64))))
(* (pow 1/4 1/4) (sqrt (/ 1 (* n (PI)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)))
(+ (* -1/4 (* (pow 1/4 1/4) (* (* k (log (* 4 (* (pow n 2) (pow (PI) 2))))) (sqrt (/ 1 (* n (PI))))))) (* (pow 1/4 1/4) (sqrt (/ 1 (* n (PI))))))
(fma.f64 k (*.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(+ (* k (+ (* -1/4 (* (pow 1/4 1/4) (* (sqrt (/ 1 (* n (PI)))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* 1/32 (* (pow 1/4 1/4) (* (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)) (sqrt (/ 1 (* n (PI))))))))) (* (pow 1/4 1/4) (sqrt (/ 1 (* n (PI))))))
(fma.f64 k (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n)))) #s(literal 2 binary64)) (*.f64 k (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/32 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (*.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n)))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(+ (* k (+ (* -1/4 (* (pow 1/4 1/4) (* (sqrt (/ 1 (* n (PI)))) (log (* 4 (* (pow n 2) (pow (PI) 2))))))) (* k (+ (* -1/384 (* (pow 1/4 1/4) (* (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3)) (sqrt (/ 1 (* n (PI))))))) (* 1/32 (* (pow 1/4 1/4) (* (sqrt (/ 1 (* n (PI)))) (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))))) (* (pow 1/4 1/4) (sqrt (/ 1 (* n (PI))))))
(fma.f64 k (fma.f64 k (fma.f64 (*.f64 (*.f64 #s(literal -1/384 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) k) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n)))) #s(literal 3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) (*.f64 (*.f64 (*.f64 #s(literal 1/32 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))) (pow.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n)))) #s(literal 2 binary64)))) (*.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n)))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1 k))))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64)))
(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1 k))))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64)))
(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1 k))))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64)))
(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ 1 k))))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64)))
(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64)))
(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64)))
(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64)))
(exp (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (- 1 (* -1 k)))))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 n n))) (fma.f64 k #s(literal -1/4 binary64) #s(literal -1/4 binary64)))

eval329.0ms (2.8%)

Memory
21.6MiB live, 603.7MiB allocated
Compiler

Compiled 40 716 to 4 466 computations (89% saved)

prune261.0ms (2.2%)

Memory
-34.5MiB live, 583.7MiB allocated
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New1 857211 878
Fresh15015
Picked505
Done000
Total1 877211 898
Accuracy
100.0%
Counts
1 898 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
55.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
37.8%
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
76.9%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
99.3%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
47.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
38.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
▶76.9%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
▶99.7%
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
▶47.1%
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
4.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
37.8%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
99.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
99.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
▶37.9%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
38.0%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
47.1%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
47.2%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
76.5%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
▶4.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
38.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
Compiler

Compiled 600 to 442 computations (26.3% saved)

simplify8.0ms (0.1%)

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

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
✓cost-diff0
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(sqrt.f64 (*.f64 (PI.f64) n))
✓cost-diff0
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
✓cost-diff0
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(/.f64 (PI.f64) k)
✓cost-diff0
(*.f64 (/.f64 (PI.f64) k) n)
✓cost-diff0
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) k)
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
✓cost-diff0
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
✓cost-diff0
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
Rules
108×lower-*.f32
90×lower-*.f64
48×*-commutative
28×lower-/.f32
20×associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028197
051197
173197
2100197
3118197
4122197
0122197
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 k)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
(*.f64 (/.f64 (PI.f64) k) n)
(/.f64 (PI.f64) k)
(PI.f64)
k
n
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 k)
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
Outputs
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 k)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (PI.f64) k)
(PI.f64)
k
n
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 k)
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) (/.f64 n k))

localize119.0ms (1%)

Memory
2.8MiB live, 313.0MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
✓accuracy99.7%
(/.f64 (*.f64 (PI.f64) n) k)
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy76.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
✓accuracy99.8%
(sqrt.f64 (*.f64 (PI.f64) n))
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.4%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
✓accuracy99.3%
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.7%
(*.f64 (/.f64 (PI.f64) k) n)
✓accuracy99.6%
(/.f64 (PI.f64) k)
✓accuracy99.3%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy76.8%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) k)
✓accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓accuracy99.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓accuracy99.7%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
✓accuracy99.7%
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓accuracy99.6%
(*.f64 (PI.f64) n)
Samples
72.0ms256×0valid
Compiler

Compiled 199 to 30 computations (84.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-sqrt: 17.0ms (35.7% of total)
ival-div: 12.0ms (25.2% of total)
ival-mult: 12.0ms (25.2% of total)
ival-pow: 4.0ms (8.4% of total)
ival-pi: 1.0ms (2.1% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series16.0ms (0.1%)

Memory
6.7MiB live, 45.7MiB allocated
Counts
18 → 348
Calls
Call 1
Inputs
#<alt (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))>
#<alt (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (/.f64 #s(literal 1 binary64) k)>
#<alt (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))>
#<alt (*.f64 (/.f64 (PI.f64) k) n)>
#<alt (/.f64 (PI.f64) k)>
#<alt (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))>
#<alt (sqrt.f64 (*.f64 (PI.f64) n))>
#<alt (*.f64 (PI.f64) n)>
#<alt (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))>
#<alt (/.f64 (*.f64 (PI.f64) n) k)>
Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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 (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (sqrt (/ 1 k))>
#<alt (/ (+ (sqrt k) (* -1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI))))))) k)>
#<alt (/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* 1/8 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 2)))))) k)>
#<alt (/ (+ (sqrt k) (* k (+ (* -1/2 (* (sqrt k) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (sqrt (pow k 3)) (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2)))))))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))))))>
#<alt (+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (/ (* 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 (/ (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 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (sqrt (/ (* n (PI)) 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))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<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))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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 (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))>
#<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 (* -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 (/ (* 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)>
Calls

87 calls:

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

rewrite367.0ms (3.1%)

Memory
-19.2MiB live, 666.3MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 796×lower-*.f32
5 780×lower-*.f64
2 392×lower-fma.f64
2 392×lower-fma.f32
1 880×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028136
051133
1145122
2697121
35661121
08099119
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
18 → 1 220
Calls
Call 1
Inputs
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
(*.f64 (/.f64 (PI.f64) k) n)
(/.f64 (PI.f64) k)
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(/.f64 (*.f64 (PI.f64) n) k)
Outputs
(exp.f64 (fma.f64 (*.f64 k #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (*.f64 k #s(literal -1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(neg.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 k)))))
(neg.f64 (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
(neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))))
(/.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 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (neg.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1 binary64)) (neg.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
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(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (neg.f64 (PI.f64))))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (neg.f64 (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (neg.f64 k)))
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64)) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 k)) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 n))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
(exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 k)) (neg.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(neg.f64 (neg.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) k) (*.f64 (PI.f64) n)))
(neg.f64 (*.f64 (/.f64 (PI.f64) (neg.f64 k)) n))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))
(/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))
(/.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (*.f64 n (neg.f64 (PI.f64))) (neg.f64 k))
(/.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (neg.f64 n) (/.f64 k (neg.f64 (PI.f64))))
(/.f64 (/.f64 (*.f64 n (neg.f64 (PI.f64))) #s(literal -1 binary64)) k)
(/.f64 (*.f64 n #s(literal -1 binary64)) (/.f64 k (neg.f64 (PI.f64))))
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (PI.f64) n))
(*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (PI.f64) n)))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (/.f64 (PI.f64) k) (/.f64 n #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) k) (*.f64 (PI.f64) n)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 n k)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) k)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) k)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) k))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (/.f64 (cbrt.f64 (PI.f64)) k) n))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) k))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) n))
(*.f64 (neg.f64 (PI.f64)) (*.f64 (/.f64 #s(literal -1 binary64) k) n))
(*.f64 (neg.f64 (PI.f64)) (*.f64 n (/.f64 #s(literal -1 binary64) k)))
(*.f64 (neg.f64 (PI.f64)) (/.f64 n (neg.f64 k)))
(*.f64 (*.f64 n (neg.f64 (PI.f64))) (/.f64 #s(literal -1 binary64) k))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (/.f64 n k) (/.f64 (PI.f64) #s(literal 1 binary64)))
(*.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (neg.f64 n) (/.f64 (PI.f64) (neg.f64 k)))
(*.f64 (/.f64 #s(literal -1 binary64) k) (*.f64 n (neg.f64 (PI.f64))))
(*.f64 (neg.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal -1 binary64))
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) k) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) k) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) k) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (*.f64 n (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) k)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) k))
(*.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) #s(literal -1 binary64)) (/.f64 (neg.f64 n) k))
(*.f64 (/.f64 n #s(literal -1 binary64)) (/.f64 (PI.f64) (neg.f64 k)))
(*.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) k) (/.f64 (*.f64 n (cbrt.f64 (PI.f64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) k) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (neg.f64 (PI.f64)) #s(literal -1 binary64)) (/.f64 n k))
(*.f64 (/.f64 (neg.f64 n) #s(literal -1 binary64)) (/.f64 (PI.f64) k))
(*.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) k))
(*.f64 (/.f64 n (neg.f64 k)) (neg.f64 (PI.f64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 n (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (/.f64 n k) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (/.f64 n (/.f64 k (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (/.f64 n (/.f64 k (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))

simplify343.0ms (2.9%)

Memory
33.9MiB live, 579.3MiB allocated
Algorithm
1×egg-herbie
Rules
10 870×lower-fma.f64
10 870×lower-fma.f32
6 378×lower-*.f64
6 378×lower-*.f32
3 008×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01523706
14173646
212203608
330473525
444613350
577913350
083323326
Stop Event
1×iter limit
1×node limit
Counts
348 → 348
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (neg.f64 (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)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 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 (fma.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) k) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (fma.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) #s(literal 1/8 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (*.f64 (fma.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k)))))) k)
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 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 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (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)) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (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)))
(* (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))))
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/ (* n (PI)) k)
(/.f64 (*.f64 n (PI.f64)) k)

eval226.0ms (1.9%)

Memory
-10.3MiB live, 380.8MiB allocated
Compiler

Compiled 34 180 to 3 185 computations (90.7% saved)

prune227.0ms (1.9%)

Memory
-35.7MiB live, 394.7MiB allocated
Pruning

28 alts after pruning (25 fresh and 3 done)

PrunedKeptTotal
New1 885191 904
Fresh10616
Picked235
Done000
Total1 897281 925
Accuracy
100.0%
Counts
1 925 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
4.9%
(pow.f64 k #s(literal -1/2 binary64))
99.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
75.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))))
55.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
99.3%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
▶47.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
38.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
▶4.9%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
76.9%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n))))
77.0%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))))
✓47.1%
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
▶99.6%
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
47.2%
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
47.2%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
47.1%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
▶4.9%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
▶99.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓37.9%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
38.0%
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
37.9%
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
47.0%
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
16.1%
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
4.9%
(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
4.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
✓4.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
38.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
15.7%
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
Compiler

Compiled 677 to 510 computations (24.7% saved)

simplify7.0ms (0.1%)

Memory
9.9MiB live, 9.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) k)
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
✓cost-diff2944
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓cost-diff0
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
✓cost-diff0
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
✓cost-diff0
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
Rules
58×lower-*.f32
40×lower-*.f64
24×*-commutative
18×lift-*.f64
14×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029181
052174
169174
283174
385174
085174
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 (*.f64 (PI.f64) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) k))
(/.f64 #s(literal 2 binary64) k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 k)
k
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
Outputs
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 (*.f64 (PI.f64) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) k))
(/.f64 #s(literal 2 binary64) k)
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 k)
k
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(PI.f64)
#s(literal 2 binary64)
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)

localize108.0ms (0.9%)

Memory
4.9MiB live, 197.3MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓accuracy99.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓accuracy99.7%
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓accuracy99.6%
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 k)
✓accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
✓accuracy99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.3%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.5%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
✓accuracy100.0%
(sqrt.f64 k)
✓accuracy99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.8%
(sqrt.f64 (*.f64 (PI.f64) n))
✓accuracy99.7%
(sqrt.f64 (/.f64 #s(literal 2 binary64) k))
✓accuracy99.7%
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
✓accuracy99.6%
(*.f64 (PI.f64) n)
Samples
60.0ms256×0valid
Compiler

Compiled 186 to 31 computations (83.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 41.0ms
ival-mult: 12.0ms (29.6% of total)
ival-sqrt: 10.0ms (24.6% of total)
ival-pow: 9.0ms (22.2% of total)
ival-div: 7.0ms (17.3% of total)
ival-pi: 1.0ms (2.5% of total)
ival-add: 1.0ms (2.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series38.0ms (0.3%)

Memory
-17.1MiB live, 61.6MiB allocated
Counts
19 → 288
Calls
Call 1
Inputs
#<alt (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))>
#<alt (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))>
#<alt (sqrt.f64 k)>
#<alt (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))>
#<alt (*.f64 (PI.f64) n)>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (/.f64 #s(literal 1 binary64) k)>
#<alt (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 (/.f64 #s(literal 2 binary64) k))>
#<alt (sqrt.f64 (*.f64 (PI.f64) n))>
#<alt (PI.f64)>
#<alt (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))>
Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))>
#<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 (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))>
#<alt (sqrt (* n (PI)))>
#<alt (+ (sqrt (* n (PI))) (* -1/2 (* (* k (log (* 2 (* n (PI))))) (sqrt (* n (PI))))))>
#<alt (+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* 2 (* n (PI)))))) (* 1/8 (* (* k (pow (log (* 2 (* n (PI)))) 2)) (sqrt (* n (PI))))))))>
#<alt (+ (sqrt (* n (PI))) (* k (+ (* -1/2 (* (sqrt (* n (PI))) (log (* 2 (* n (PI)))))) (* k (+ (* -1/48 (* (* k (pow (log (* 2 (* n (PI)))) 3)) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (pow (log (* 2 (* n (PI)))) 2))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))))))>
#<alt (+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (exp (* -1/2 (* k (log (* 2 (* n (PI)))))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<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 (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (sqrt (/ 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 (pow (/ 1 k) 1/4)>
#<alt (pow (/ 1 k) 1/4)>
#<alt (pow (/ 1 k) 1/4)>
#<alt (pow (/ 1 k) 1/4)>
#<alt (pow (/ 1 k) 1/4)>
#<alt (pow (/ 1 k) 1/4)>
#<alt (pow (/ 1 k) 1/4)>
#<alt (pow (/ 1 k) 1/4)>
#<alt (* (pow (/ -1 k) 1/4) (sqrt (/ 1 (sqrt -1))))>
#<alt (* (pow (/ -1 k) 1/4) (sqrt (/ 1 (sqrt -1))))>
#<alt (* (pow (/ -1 k) 1/4) (sqrt (/ 1 (sqrt -1))))>
#<alt (* (pow (/ -1 k) 1/4) (sqrt (/ 1 (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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 (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 k)) (pow (sqrt -1) 2))>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (/ 1 k)>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (* (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 (* 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

72 calls:

TimeVariablePointExpression
16.0ms
k
@0
(sqrt (/ 1 (sqrt k)))
6.0ms
k
@inf
(sqrt (/ 1 (sqrt k)))
1.0ms
n
@-inf
(* (* (pow (* 2 (* (PI) n)) (* k -1/2)) (sqrt (* (PI) n))) (sqrt (/ 2 k)))
1.0ms
k
@-inf
(* (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ (* k -1/2) 1/2)))
1.0ms
n
@-inf
(* (sqrt (/ 1 k)) (pow (* n (* (PI) 2)) (+ (* k -1/2) 1/2)))

rewrite326.0ms (2.8%)

Memory
30.3MiB live, 418.5MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 984×lower-*.f32
5 966×lower-*.f64
2 798×lower-fma.f32
2 796×lower-fma.f64
2 188×lower-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029133
052129
1171113
2874112
37496112
08376112
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
19 → 1 179
Calls
Call 1
Inputs
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 (PI.f64) n)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) k))
(sqrt.f64 (*.f64 (PI.f64) n))
(PI.f64)
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
Outputs
(exp.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 k) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(exp.f64 (fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(neg.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64)))))))
(neg.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (sqrt.f64 k))) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (sqrt.f64 k))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 (neg.f64 k)))
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(+.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
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(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))))
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(*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (sqrt.f64 (PI.f64))))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
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(*.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 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.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 n (cbrt.f64 (PI.f64))) #s(literal 2 binary64)))
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(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) n))
(*.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 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64))))
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(*.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (exp.f64 (log.f64 (*.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 (PI.f64) n))))
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(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))

simplify269.0ms (2.3%)

Memory
9.0MiB live, 440.0MiB allocated
Algorithm
1×egg-herbie
Rules
7 094×lower-fma.f64
7 094×lower-fma.f32
4 894×lower-*.f64
4 894×lower-*.f32
1 936×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01993398
15803310
217433235
329422977
448692977
083472907
Stop Event
1×iter limit
1×node limit
Counts
288 → 288
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))
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(* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (log (* 2 (* n (PI))))))))
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))
(exp (* -1/2 (* k (+ (log n) (log (* 2 (PI)))))))
(exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
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(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
1
(+ 1 (* -1/2 (* k (log (* 2 (* n (PI)))))))
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* 1/8 (* k (pow (log (* 2 (* n (PI)))) 2))))))
(+ 1 (* k (+ (* -1/2 (log (* 2 (* n (PI))))) (* k (+ (* -1/48 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/8 (pow (log (* 2 (* n (PI)))) 2)))))))
(exp (* -1/2 (* k (log (* 2 (* n (PI)))))))
(exp (* -1/2 (* k (log (* 2 (* n (PI)))))))
(exp (* -1/2 (* k (log (* 2 (* n (PI)))))))
(exp (* -1/2 (* k (log (* 2 (* n (PI)))))))
(exp (* -1/2 (* k (log (* 2 (* n (PI)))))))
(exp (* -1/2 (* k (log (* 2 (* n (PI)))))))
(exp (* -1/2 (* k (log (* 2 (* n (PI)))))))
(exp (* -1/2 (* k (log (* 2 (* n (PI)))))))
(* 2 (* n (PI)))
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(sqrt (/ 1 k))
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(sqrt (/ 1 k))
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(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
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(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
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(* n (PI))
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(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))
(pow (/ 1 k) 1/4)
(pow (/ 1 k) 1/4)
(pow (/ 1 k) 1/4)
(pow (/ 1 k) 1/4)
(pow (/ 1 k) 1/4)
(pow (/ 1 k) 1/4)
(pow (/ 1 k) 1/4)
(pow (/ 1 k) 1/4)
(* (pow (/ -1 k) 1/4) (sqrt (/ 1 (sqrt -1))))
(* (pow (/ -1 k) 1/4) (sqrt (/ 1 (sqrt -1))))
(* (pow (/ -1 k) 1/4) (sqrt (/ 1 (sqrt -1))))
(* (pow (/ -1 k) 1/4) (sqrt (/ 1 (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(sqrt (/ 1 k))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(/ 1 k)
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* (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)))
(* 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)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (pow (sqrt -1) 2) (sqrt 2)))))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (*.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)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k)))) (*.f64 (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) (*.f64 k (*.f64 k k))))) #s(literal 1/8 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 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 (fma.f64 k (fma.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64)) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) #s(literal -1/48 binary64))))) (*.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 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) k)
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(*.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)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64)))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (pow (sqrt -1) 2))))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
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(* 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)))

eval244.0ms (2.1%)

Memory
16.8MiB live, 512.3MiB allocated
Compiler

Compiled 37 475 to 3 713 computations (90.1% saved)

prune271.0ms (2.3%)

Memory
8.3MiB live, 464.5MiB allocated
Pruning

40 alts after pruning (32 fresh and 8 done)

PrunedKeptTotal
New2 012162 028
Fresh41620
Picked055
Done033
Total2 016402 056
Accuracy
100.0%
Counts
2 056 → 40
Alt Table
Click to see full alt table
StatusAccuracyProgram
4.9%
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -2 binary64))
4.9%
(pow.f64 k #s(literal -1/2 binary64))
99.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
75.5%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
55.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
47.0%
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
99.3%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
✓47.2%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
4.9%
(/.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 k)))
38.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
4.9%
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
4.9%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
99.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
4.9%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
4.9%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))
✓4.9%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
76.9%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n))))
77.0%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))))
✓47.1%
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
46.9%
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k))))
4.9%
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
✓99.6%
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
4.9%
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
4.9%
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
47.2%
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
47.2%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
47.1%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
4.9%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
✓4.9%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
✓99.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓37.9%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
38.0%
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
37.9%
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
4.9%
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
4.9%
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 k))))
16.1%
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
38.0%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
4.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
✓4.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
15.7%
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
Compiler

Compiled 1 564 to 629 computations (59.8% saved)

regimes95.0ms (0.8%)

Memory
-23.3MiB live, 169.6MiB allocated
Counts
77 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k))))
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -2 binary64))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 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) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.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 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -4 binary64)))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 k (*.f64 (PI.f64) (*.f64 k n))))) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 k n))))) k)
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
Outputs
(/.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 1/2 binary64)))))
Calls

4 calls:

26.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms
n
22.0ms
k
19.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.7%1k
99.7%1n
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes90.0ms (0.8%)

Memory
34.6MiB live, 150.8MiB allocated
Counts
68 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k))))
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -2 binary64))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 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) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
Outputs
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
Calls

4 calls:

25.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms
n
22.0ms
k
17.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.7%1k
99.7%1n
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes105.0ms (0.9%)

Memory
-26.1MiB live, 154.4MiB allocated
Counts
67 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k))))
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -2 binary64))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 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) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
Outputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
Calls

4 calls:

38.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms
n
22.0ms
k
20.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%1k
99.6%1n
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
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))))
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes122.0ms (1%)

Memory
-6.1MiB live, 77.6MiB allocated
Counts
65 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k))))
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -2 binary64))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 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) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 k #s(literal -1 binary64)))))
Outputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
Calls

4 calls:

43.0ms
n
41.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms
k
16.0ms
(*.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
99.5%1k
99.5%1n
99.5%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes112.0ms (0.9%)

Memory
-14.1MiB live, 61.9MiB allocated
Counts
44 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k))))
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -2 binary64))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k))
Calls

4 calls:

43.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
41.0ms
k
13.0ms
n
12.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
98.2%2k
55.6%1n
98.2%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
55.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes48.0ms (0.4%)

Memory
15.3MiB live, 53.8MiB allocated
Counts
43 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k))))
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 k)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(sqrt.f64 (pow.f64 (sqrt.f64 k) #s(literal -2 binary64)))
(pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal -2 binary64))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64)))
Outputs
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
Calls

2 calls:

33.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
12.0ms
k
Results
AccuracySegmentsBranch
59.4%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
59.3%2k
Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes56.0ms (0.5%)

Memory
-18.7MiB live, 23.1MiB allocated
Counts
34 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 k)))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 k))))
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 k)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))))
Outputs
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
Calls

2 calls:

44.0ms
(*.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))))
10.0ms
k
Results
AccuracySegmentsBranch
59.0%2k
59.0%2(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes59.0ms (0.5%)

Memory
-4.2MiB live, 35.1MiB allocated
Counts
18 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)) n)) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
Calls

4 calls:

6.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
6.0ms
k
6.0ms
n
6.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
47.2%1n
47.2%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
47.2%1k
47.2%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes10.0ms (0.1%)

Memory
20.7MiB live, 20.7MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k #s(literal 1/2 binary64))))
Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
Calls

4 calls:

2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
n
2.0ms
k
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
38.0%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
38.0%1k
38.0%1n
38.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes8.0ms (0.1%)

Memory
16.7MiB live, 16.7MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
3 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
Outputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
Calls

4 calls:

2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms
n
2.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
2.0ms
k
Results
AccuracySegmentsBranch
4.9%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))))
4.9%1k
4.9%1n
4.9%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

bsearch42.0ms (0.4%)

Memory
-9.7MiB live, 28.1MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
40.0ms
0.0056745448713748994
1.9468801014156354
Samples
35.0ms128×0valid
Compiler

Compiled 237 to 194 computations (18.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-pow: 26.0ms (82.3% of total)
ival-div: 2.0ms (6.3% of total)
ival-mult: 2.0ms (6.3% of total)
ival-sub: 1.0ms (3.2% of total)
ival-sqrt: 1.0ms (3.2% 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)

bsearch0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
8.57976093497905e-139
Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
8.57976093497905e-139
Compiler

Compiled 21 to 18 computations (14.3% saved)

simplify25.0ms (0.2%)

Memory
-23.7MiB live, 14.1MiB allocated
Algorithm
1×egg-herbie
Rules
30×*-commutative_binary64
4×+-commutative_binary64
4×sub-neg_binary64
2×1-exp_binary64
2×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056187
174187
278187
380187
481187
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.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 1/2 binary64)))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 1 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
Outputs
(/.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 1/2 binary64)))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 1 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(if (<=.f64 k #s(literal 1 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))

soundness1.1s (9.4%)

Memory
26.6MiB live, 662.4MiB allocated
Rules
9 974×lower-fma.f64
9 974×lower-fma.f32
8 506×lower-fma.f64
8 506×lower-fma.f32
8 436×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04065392
112845172
247865053
091144886
01343
02243
18940
249738
3447438
0859937
01281174
13451155
210111065
333481038
45547966
08354945
028136
051133
1145122
2697121
35661121
08099119
040179
072169
1269160
21583153
08282151
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 463 to 262 computations (43.4% saved)

preprocess200.0ms (1.7%)

Memory
9.5MiB live, 160.8MiB allocated
Compiler

Compiled 414 to 138 computations (66.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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