Migdal et al, Equation (51)

Time bar (total: 11.7s)

analyze178.0ms (1.5%)

Memory
4.5MiB live, 202.9MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
50%25%25%0.1%0%50%0%6
51.6%25%23.4%0.1%0%51.5%0%7
52.5%25%22.6%0.1%0%52.3%0%8
53.8%25%21.5%0.1%0%53.5%0%9
54.5%25%20.9%0.1%0%54%0%10
55.3%25%20.2%0.1%0%54.7%0%11
55.7%25%19.9%0.1%0%55.1%0%12
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.2s (27.8%)

Memory
74.7MiB live, 4 780.2MiB allocated
Samples
1.0s8 256×0valid
755.0ms3 478×1invalid
301.0ms1 882×1exit
135.0ms427×2invalid
55.0ms499×0invalid
25.0ms215×0exit
Precisions
Click to see histograms. Total time spent on operations: 1.6s
ival-pow: 423.0ms (26% of total)
ival-mult: 410.0ms (25.2% of total)
ival-div: 288.0ms (17.7% of total)
ival-sub: 176.0ms (10.8% of total)
ival-sqrt: 122.0ms (7.5% of total)
adjust: 99.0ms (6.1% of total)
ival-pi: 70.0ms (4.3% of total)
exact: 20.0ms (1.2% of total)
ival-true: 12.0ms (0.7% of total)
ival-assert: 6.0ms (0.4% of total)
Bogosity

preprocess54.0ms (0.5%)

Memory
-18.2MiB live, 34.8MiB 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))

explain348.0ms (3%)

Memory
6.9MiB live, 284.7MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
699(1.0136634477991624e-298 2.0019137856956743e+190)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)))sensitivity10526
Confusion
Predicted +Predicted -
+60
-99151
Precision
0.05714285714285714
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+600
-9926125
Precision?
0.04580152671755725
Recall?
1.0
Freqs
test
numberfreq
0151
1105
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
71.0ms512×0valid
Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 52.0ms
ival-pow: 25.0ms (48.4% of total)
ival-mult: 8.0ms (15.5% of total)
ival-div: 7.0ms (13.5% of total)
ival-sub: 4.0ms (7.7% of total)
ival-sqrt: 4.0ms (7.7% of total)
ival-pi: 2.0ms (3.9% of total)
exact: 1.0ms (1.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify21.0ms (0.2%)

Memory
-23.1MiB live, 17.5MiB 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)

localize70.0ms (0.6%)

Memory
30.5MiB live, 69.9MiB 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))))
✓accuracy99.6%
(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
56.0ms256×0valid
Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-pow: 5.0ms (28.7% of total)
ival-mult: 4.0ms (23% of total)
ival-div: 3.0ms (17.2% of total)
ival-sqrt: 2.0ms (11.5% of total)
ival-pi: 1.0ms (5.7% of total)
ival-sub: 1.0ms (5.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series157.0ms (1.3%)

Memory
6.7MiB live, 124.9MiB 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
62.0ms
n
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
40.0ms
k
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
28.0ms
n
@inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
22.0ms
n
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms
k
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite477.0ms (4.1%)

Memory
-32.1MiB live, 443.9MiB 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)))))

simplify606.0ms (5.2%)

Memory
30.6MiB live, 465.8MiB 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)))

eval67.0ms (0.6%)

Memory
0.4MiB live, 152.2MiB allocated
Compiler

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

prune78.0ms (0.7%)

Memory
-8.5MiB live, 189.7MiB allocated
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New49916515
Fresh000
Picked101
Done000
Total50016516
Accuracy
100.0%
Counts
516 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.4%
(/.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))
48.8%
(/.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)
▶99.6%
(/.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)))))
99.4%
(/.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))))))
▶55.8%
(*.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
67.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (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))))))
▶99.3%
(*.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))))
▶46.6%
(*.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)))
56.9%
(*.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)))
99.3%
(*.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))))))
99.3%
(*.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)))))
99.5%
(*.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)))))
56.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
55.9%
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 #s(literal 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))))
▶43.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
99.4%
(*.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 678 to 466 computations (31.3% saved)

simplify11.0ms (0.1%)

Memory
24.1MiB live, 24.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
✓cost-diff0
(fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(*.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 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 (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))))
✓cost-diff1088
(/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n))
✓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
140×lower-*.f32
114×lower-*.f64
58×*-commutative
48×lower-/.f32
36×lower-/.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
039256
070254
1105246
2137246
3166246
4183246
5187246
0187246
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)) (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 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
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 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n))
(*.f64 (PI.f64) #s(literal -2 binary64))
(PI.f64)
#s(literal -2 binary64)
(/.f64 #s(literal -1 binary64) n)
#s(literal -1 binary64)
n
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#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))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
n
(fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))
k
#s(literal 1/2 binary64)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(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)))))
(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 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.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)) (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 (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 (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)))
(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 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal -2 binary64))
(PI.f64)
#s(literal -2 binary64)
(/.f64 #s(literal -1 binary64) n)
#s(literal -1 binary64)
n
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(*.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
n
(fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))
k
#s(literal 1/2 binary64)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(sqrt.f64 k)

localize186.0ms (1.6%)

Memory
-33.8MiB live, 303.2MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
✓accuracy99.3%
(*.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
✓accuracy99.1%
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓accuracy81.5%
(PI.f64)
✓accuracy99.6%
(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)))
✓accuracy99.6%
(/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy81.5%
(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)))
✓accuracy99.7%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy81.5%
(PI.f64)
✓accuracy99.7%
(*.f64 n (PI.f64))
✓accuracy99.4%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy86.3%
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓accuracy81.5%
(PI.f64)
✓accuracy99.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓accuracy99.7%
(*.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)))))
✓accuracy81.5%
(PI.f64)
Samples
91.0ms207×0valid
17.0ms49×0exit
Compiler

Compiled 267 to 41 computations (84.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 83.0ms
ival-mult: 39.0ms (46.9% of total)
ival-pow: 22.0ms (26.4% of total)
ival-div: 9.0ms (10.8% of total)
ival-sqrt: 7.0ms (8.4% of total)
ival-pi: 3.0ms (3.6% of total)
ival-add: 3.0ms (3.6% of total)
exact: 1.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series108.0ms (0.9%)

Memory
11.2MiB live, 243.7MiB allocated
Counts
22 → 372
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 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n))>
#<alt (*.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))))>
#<alt (*.f64 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))>
#<alt (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))>
#<alt (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))>
#<alt (PI.f64)>
#<alt (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)>
#<alt (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)))>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 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))))))))>
#<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 (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (exp (* -1/2 (* 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 (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 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)) (* (exp (* (log n) (+ 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* 1/2 k))))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* 1/2 k))))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* 1/2 k))))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* 1/2 k))))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2))))))) k)>
#<alt (/ (+ (* k (+ (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log n) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log n) 3) (sqrt 2)))) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (* n (PI))) (* (log n) (* (pow (log (* 2 (PI))) 2) (sqrt 2))))) (* 1/16 (* (sqrt (* n (PI))) (* (pow (log n) 2) (* (log (* 2 (PI))) (sqrt 2))))))))))) (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log n) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (+ 1/2 (* 1/2 k)))) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (- 1/2 (* -1/2 k)))) (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (- 1/2 (* -1/2 k)))) (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (- 1/2 (* -1/2 k)))) (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))))>
#<alt (* (sqrt (/ 1 k)) (* (exp (* (log n) (- 1/2 (* -1/2 k)))) (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))))>
#<alt (exp (* (log n) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log n) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log n) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log n) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* 1/2 k)))))>
#<alt (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* 1/2 k)))))>
#<alt (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* 1/2 k)))))>
#<alt (exp (* -1 (* (log (/ 1 n)) (+ 1/2 (* 1/2 k)))))>
#<alt (exp (* (+ 1/2 (* 1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* 1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* 1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* 1/2 k)) (+ (log -1) (* -1 (log (/ -1 n))))))>
#<alt (sqrt n)>
#<alt (+ (sqrt n) (* 1/2 (* (* k (log n)) (sqrt n))))>
#<alt (+ (sqrt n) (* k (+ (* 1/8 (* (* k (pow (log n) 2)) (sqrt n))) (* 1/2 (* (sqrt n) (log n))))))>
#<alt (+ (sqrt n) (* k (+ (* 1/2 (* (sqrt n) (log n))) (* k (+ (* 1/48 (* (* k (pow (log n) 3)) (sqrt n))) (* 1/8 (* (sqrt n) (pow (log n) 2))))))))>
#<alt (exp (* (log n) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log n) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log n) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log n) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log n) (- 1/2 (* -1/2 k))))>
#<alt (exp (* (log n) (- 1/2 (* -1/2 k))))>
#<alt (exp (* (log n) (- 1/2 (* -1/2 k))))>
#<alt (exp (* (log n) (- 1/2 (* -1/2 k))))>
#<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 (* 1/2 (/ 1 k))))>
#<alt (* k (+ 1/2 (* 1/2 (/ 1 k))))>
#<alt (* k (+ 1/2 (* 1/2 (/ 1 k))))>
#<alt (* 1/2 k)>
#<alt (* k (+ 1/2 (* 1/2 (/ 1 k))))>
#<alt (* k (+ 1/2 (* 1/2 (/ 1 k))))>
#<alt (* k (+ 1/2 (* 1/2 (/ 1 k))))>
#<alt (* (sqrt (/ (PI) k)) (sqrt 2))>
#<alt (/ (+ (* 1/2 (* (sqrt (* (pow k 3) (PI))) (* (log (* 2 (PI))) (sqrt 2)))) (* (sqrt (* k (PI))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* 1/8 (* (sqrt (* (pow k 3) (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* k (PI))) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (* k (PI))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* 1/2 (* (sqrt (* k (PI))) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* 1/48 (* (sqrt (* (pow k 3) (PI))) (* (pow (log (* 2 (PI))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (PI))) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))))))) (* (sqrt (* k (PI))) (sqrt 2))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k)))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (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 (PI)) (sqrt 2))>
#<alt (+ (* 1/2 (* (* k (* (log (* 2 (PI))) (sqrt 2))) (sqrt (PI)))) (* (sqrt (PI)) (sqrt 2)))>
#<alt (+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (PI))) 2) (sqrt 2))) (sqrt (PI)))) (* 1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))))) (* (sqrt (PI)) (sqrt 2)))>
#<alt (+ (* k (+ (* 1/2 (* (sqrt (PI)) (* (log (* 2 (PI))) (sqrt 2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (PI))) 3) (sqrt 2))) (sqrt (PI)))) (* 1/8 (* (sqrt (PI)) (* (pow (log (* 2 (PI))) 2) (sqrt 2)))))))) (* (sqrt (PI)) (sqrt 2)))>
#<alt (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))>
Calls

93 calls:

TimeVariablePointExpression
37.0ms
n
@-inf
(* (pow n (+ (* k 1/2) 1/2)) (/ (pow (* 2 (PI)) (+ (* k 1/2) 1/2)) (sqrt k)))
22.0ms
n
@0
(* (pow n (+ (* k 1/2) 1/2)) (/ (pow (* 2 (PI)) (+ (* k 1/2) 1/2)) (sqrt k)))
7.0ms
n
@inf
(* (pow n (+ (* k 1/2) 1/2)) (/ (pow (* 2 (PI)) (+ (* k 1/2) 1/2)) (sqrt k)))
4.0ms
k
@inf
(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
3.0ms
k
@0
(pow n (+ (* k 1/2) 1/2))

rewrite281.0ms (2.4%)

Memory
-7.9MiB live, 547.0MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 920×lower-*.f32
4 894×lower-*.f64
3 630×lower-/.f32
3 618×lower-/.f64
2 128×lower-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
039174
070174
1250163
21521149
08343149
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
22 → 1 432
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 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) 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 (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(PI.f64)
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(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)))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
Outputs
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (fma.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (log.f64 n) (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)) #s(literal -1 binary64))))
(exp.f64 (fma.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 (PI.f64) (*.f64 #s(literal 2 binary64) n))))))
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(exp.f64 (*.f64 (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
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(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 k #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))))
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(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 k #s(literal 1 binary64))))
(neg.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
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(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 k #s(literal 1 binary64)))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 k #s(literal 1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k (*.f64 k #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 k k)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 k (*.f64 k #s(literal 1/4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 k k)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 k (*.f64 k #s(literal 1/4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal -1/4 binary64))))))
(pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 k #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 k #s(literal 1 binary64))) (pow.f64 (PI.f64) (+.f64 k #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 (PI.f64) (+.f64 k #s(literal 1 binary64))) (pow.f64 #s(literal 2 binary64) (+.f64 k #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(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))))
(*.f64 #s(literal -1 binary64) (neg.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 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (exp.f64 (*.f64 (*.f64 k #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 (fma.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64))))
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(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 k #s(literal -1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 k #s(literal -1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 k #s(literal -1/4 binary64)))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 k #s(literal -1/4 binary64)))))

simplify417.0ms (3.6%)

Memory
10.2MiB live, 794.3MiB allocated
Algorithm
1×egg-herbie
Rules
14 516×lower-fma.f64
14 516×lower-fma.f32
6 950×lower-*.f64
6 950×lower-*.f32
4 644×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03874873
112484677
241744404
080294241
Stop Event
1×iter limit
1×node limit
Counts
372 → 372
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
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(exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))
(exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))
(exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))
(exp (* (log (* 2 (PI))) (+ 1/2 (* 1/2 k))))
(exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))
(exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))
(exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))
(exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))
Outputs
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (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 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (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 (* (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 (*.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 (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)) #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 (* (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 k (neg.f64 (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/8 binary64))) (+.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 k (*.f64 k k)))) (*.f64 #s(literal -1/2 binary64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))) (*.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 3 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/24 binary64)))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 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)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* 2 (* n (PI)))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* 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)) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
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(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (log (* 2 (PI))) (- 1/2 (* -1/2 k))))
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

eval557.0ms (4.8%)

Memory
-140.0MiB live, 519.3MiB allocated
Compiler

Compiled 48 283 to 4 532 computations (90.6% saved)

prune275.0ms (2.4%)

Memory
-44.8MiB live, 445.0MiB allocated
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New2 270162 286
Fresh10111
Picked415
Done000
Total2 284182 302
Accuracy
100.0%
Counts
2 302 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.4%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
▶99.6%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
57.0%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
46.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
▶56.9%
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
56.7%
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
56.8%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
5.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(literal 1 binary64))
✓43.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
57.0%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64)))
99.4%
(*.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))))
▶43.5%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
57.0%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
57.0%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
99.6%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
79.2%
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
43.6%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
▶5.4%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
Compiler

Compiled 459 to 353 computations (23.1% saved)

simplify8.0ms (0.1%)

Memory
12.4MiB live, 12.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓cost-diff0
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 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
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (/.f64 n k))
✓cost-diff0
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) k)
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓cost-diff0
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
✓cost-diff0
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
Rules
56×lower-*.f32
42×lower-*.f64
26×*-commutative
18×lower-/.f32
14×lift-sqrt.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029174
053174
169174
280174
382174
082174
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(PI.f64)
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
(*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
k
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(PI.f64)
(/.f64 n k)
n
k
(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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(PI.f64)
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
k
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 k)
Outputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(PI.f64)
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
(sqrt.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
k
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n 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 (PI.f64) (/.f64 n k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (*.f64 (PI.f64) n) k)
(PI.f64)
(/.f64 n k)
n
k
(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 #s(literal 2 binary64)) (/.f64 (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 (PI.f64) (*.f64 #s(literal 2 binary64) 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))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(PI.f64)
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
k
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 k)

localize111.0ms (1%)

Memory
15.4MiB live, 205.1MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓accuracy99.7%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
✓accuracy99.6%
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓accuracy81.5%
(PI.f64)
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.6%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
✓accuracy99.4%
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy81.5%
(PI.f64)
✓accuracy99.7%
(*.f64 (PI.f64) (/.f64 n k))
✓accuracy99.4%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy86.3%
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
✓accuracy81.5%
(PI.f64)
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) k)
✓accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓accuracy99.8%
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
✓accuracy99.7%
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓accuracy99.7%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
✓accuracy81.5%
(PI.f64)
Samples
52.0ms207×0valid
15.0ms49×0exit
Compiler

Compiled 179 to 32 computations (82.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
ival-mult: 14.0ms (29.5% of total)
ival-sqrt: 11.0ms (23.2% of total)
ival-div: 10.0ms (21.1% of total)
ival-pow: 8.0ms (16.9% of total)
ival-pi: 1.0ms (2.1% of total)
ival-add: 1.0ms (2.1% of total)
exact: 1.0ms (2.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series22.0ms (0.2%)

Memory
-4.4MiB live, 33.3MiB allocated
Counts
15 → 264
Calls
Call 1
Inputs
#<alt (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))>
#<alt (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))>
#<alt (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))>
#<alt (PI.f64)>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (/.f64 #s(literal 1 binary64) k)>
#<alt (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))>
#<alt (*.f64 (PI.f64) (/.f64 n 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))>
#<alt (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))>
Outputs
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (sqrt (/ 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 (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (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 (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
Calls

66 calls:

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

rewrite312.0ms (2.7%)

Memory
2.9MiB live, 476.7MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
6 962×lower-*.f32
6 950×lower-*.f64
3 044×lower-/.f32
3 034×lower-/.f64
1 826×lower-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029103
053101
1171100
292294
0831794
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
15 → 1 083
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(PI.f64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))))
(exp.f64 (fma.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 k))) (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))) (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(neg.f64 (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64))) (sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (neg.f64 k))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))) (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal 1/2 binary64)))))
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(*.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
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(*.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))

simplify406.0ms (3.5%)

Memory
10.8MiB live, 656.2MiB allocated
Algorithm
1×egg-herbie
Rules
14 236×lower-fma.f64
14 236×lower-fma.f32
5 826×lower-*.f64
5 826×lower-*.f32
2 808×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01922907
15882818
220382768
344722584
082312525
Stop Event
1×iter limit
1×node limit
Counts
264 → 264
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
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(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
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(* n (PI))
(* n (PI))
(* n (PI))
(* n (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 n) (log (* 2 (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
Outputs
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) 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 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (*.f64 k (*.f64 k k))))) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)) (*.f64 (*.f64 (*.f64 k k) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(/.f64 (fma.f64 (*.f64 k k) (*.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 n (fma.f64 (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) #s(literal 1/6 binary64) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)))) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 n (PI.f64)) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 n (PI.f64)) k)))))) k (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) k)))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* (sqrt (* n (PI))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
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(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(* 2 (* n (PI)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))
(sqrt (/ 1 k))
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(sqrt (/ 1 k))
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(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
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(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
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(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
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(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(/ 1 k)
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(/ 1 k)
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(/ 1 k)
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #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 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))))) k (fma.f64 k (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) k))) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 #s(literal -1/48 binary64) k) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal 1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (fma.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (*.f64 (*.f64 n (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 (* 1/2 k))))
(pow.f64 (*.f64 (*.f64 n (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 (* 1/2 k))))
(pow.f64 (*.f64 (*.f64 n (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 (* 1/2 k))))
(pow.f64 (*.f64 (*.f64 n (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 (* -1/2 k))))
(pow.f64 (*.f64 (*.f64 n (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 (* -1/2 k))))
(pow.f64 (*.f64 (*.f64 n (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 (* -1/2 k))))
(pow.f64 (*.f64 (*.f64 n (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 (* -1/2 k))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))

eval231.0ms (2%)

Memory
9.5MiB live, 346.2MiB allocated
Compiler

Compiled 28 565 to 3 214 computations (88.7% saved)

prune195.0ms (1.7%)

Memory
1.4MiB live, 331.2MiB allocated
Pruning

25 alts after pruning (22 fresh and 3 done)

PrunedKeptTotal
New1 628171 645
Fresh7512
Picked235
Done101
Total1 638251 663
Accuracy
100.0%
Counts
1 663 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶14.1%
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
5.4%
(pow.f64 k #s(literal -1/2 binary64))
✓99.4%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
▶56.9%
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
57.0%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
46.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
▶5.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
79.2%
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
56.7%
(*.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
56.7%
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
▶43.3%
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
57.0%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
5.4%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
99.4%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓43.5%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
86.1%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
▶99.7%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
57.0%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
57.0%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
14.9%
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
86.3%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
43.6%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
5.4%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
✓5.4%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
14.1%
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
Compiler

Compiled 588 to 428 computations (27.2% saved)

simplify7.0ms (0.1%)

Memory
13.1MiB live, 13.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 #s(literal 1 binary64) k)
✓cost-diff0
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
✓cost-diff704
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))
✓cost-diff0
(sqrt.f64 (*.f64 n (PI.f64)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
✓cost-diff0
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
✓cost-diff0
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
✓cost-diff0
(/.f64 n k)
✓cost-diff0
(sqrt.f64 (/.f64 n k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff0
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) n)
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) n))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
Rules
60×lower-*.f32
42×lower-*.f64
26×lower-/.f32
20×*-commutative
18×lift-*.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
029161
053161
172157
283157
387157
087157
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
(PI.f64)
(*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
k
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
n
k
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
n
(PI.f64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
#s(literal 1/4 binary64)
Outputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(PI.f64)
(*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))
k
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
n
k
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(PI.f64)
#s(literal 2 binary64)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
n
(PI.f64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 k k)) #s(literal 1/4 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) (*.f64 k k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
#s(literal 1/4 binary64)

localize105.0ms (0.9%)

Memory
-13.0MiB live, 181.9MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) k)
✓accuracy99.6%
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))
✓accuracy62.3%
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
✓accuracy99.7%
(*.f64 n (PI.f64))
✓accuracy99.6%
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
✓accuracy99.4%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
✓accuracy81.5%
(PI.f64)
✓accuracy99.4%
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
✓accuracy98.7%
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
✓accuracy86.3%
(sqrt.f64 (/.f64 n k))
✓accuracy81.5%
(PI.f64)
✓accuracy100.0%
(sqrt.f64 k)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.7%
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
✓accuracy99.7%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
✓accuracy99.7%
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
✓accuracy81.5%
(PI.f64)
Samples
49.0ms207×0valid
11.0ms49×0exit
Compiler

Compiled 163 to 31 computations (81% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-sqrt: 13.0ms (30.3% of total)
ival-mult: 12.0ms (28% of total)
ival-pow: 9.0ms (21% of total)
ival-div: 8.0ms (18.7% of total)
ival-pi: 1.0ms (2.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series46.0ms (0.4%)

Memory
4.6MiB live, 80.0MiB allocated
Counts
21 → 300
Calls
Call 1
Inputs
#<alt (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) n))>
#<alt (*.f64 #s(literal 2 binary64) n)>
#<alt (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))>
#<alt (sqrt.f64 k)>
#<alt (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))>
#<alt (sqrt.f64 (/.f64 n k))>
#<alt (/.f64 n k)>
#<alt (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 (*.f64 n (PI.f64)))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))>
#<alt (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))>
#<alt (/.f64 #s(literal 1 binary64) k)>
#<alt (PI.f64)>
#<alt (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))>
#<alt (*.f64 n (PI.f64))>
Outputs
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt n) (sqrt 2))>
#<alt (* (sqrt n) (sqrt 2))>
#<alt (* (sqrt n) (sqrt 2))>
#<alt (* (sqrt n) (sqrt 2))>
#<alt (* (sqrt n) (sqrt 2))>
#<alt (* (sqrt n) (sqrt 2))>
#<alt (* (sqrt n) (sqrt 2))>
#<alt (* (sqrt n) (sqrt 2))>
#<alt (* -1 (* (sqrt n) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt n) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt n) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt n) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (* 2 n)>
#<alt (sqrt (/ (PI) k))>
#<alt (/ (+ (sqrt (* k (PI))) (* -1/2 (* (sqrt (* (pow k 3) (PI))) (log (* 2 (* n (PI))))))) k)>
#<alt (/ (+ (sqrt (* k (PI))) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (PI))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* -1/2 (* (sqrt (/ (PI) k)) (log (* 2 (* n (PI))))))))) k)>
#<alt (/ (+ (sqrt (* k (PI))) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (PI) k)) (log (* 2 (* n (PI)))))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* -1/2 (* (sqrt (/ k (PI))) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* -1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (+ (* 1/6 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (* 1/4 (/ (* (PI) (pow (log (* 2 (* n (PI)))) 2)) k)))))))))))) k)>
#<alt (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (pow (sqrt -1) 2))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (sqrt (/ (PI) (* k (exp (* 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))>
#<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)) (* (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 k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ n k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (sqrt (/ n k))>
#<alt (* (sqrt (/ n k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ n k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ n k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ n k)) (pow (sqrt -1) 2))>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (/ n k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (/ 1 (pow k 2))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (* (sqrt (/ 1 k)) (sqrt -1))>
#<alt (* (sqrt (/ 1 k)) (sqrt -1))>
#<alt (* (sqrt (/ 1 k)) (sqrt -1))>
#<alt (* (sqrt (/ 1 k)) (sqrt -1))>
#<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 (* 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 (/ (PI) k)>
#<alt (/ (+ (PI) (* -1 (* k (* (PI) (log (* 2 (* n (PI)))))))) k)>
#<alt (/ (+ (PI) (* k (- (* -1 (* k (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* (PI) (log (* 2 (* n (PI)))))))) k)>
#<alt (/ (+ (PI) (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* -1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (* 1/6 (* (PI) (pow (log (* 2 (* n (PI)))) 3))))))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* (PI) (log (* 2 (* n (PI)))))))) k)>
#<alt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))>
#<alt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))>
#<alt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))>
#<alt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))>
#<alt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))>
#<alt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))>
#<alt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))>
#<alt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))>
#<alt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
Calls

75 calls:

TimeVariablePointExpression
25.0ms
k
@0
(pow (* (/ 1 k) (/ 1 k)) 1/4)
1.0ms
k
@0
(sqrt (/ (PI) (* k (pow (* (PI) (* 2 n)) k))))
1.0ms
k
@-inf
(sqrt (/ (PI) (* k (pow (* (PI) (* 2 n)) k))))
1.0ms
k
@inf
(sqrt (/ (PI) (* k (pow (* (PI) (* 2 n)) k))))
1.0ms
n
@-inf
(sqrt (/ (PI) (* k (pow (* (PI) (* 2 n)) k))))

rewrite317.0ms (2.7%)

Memory
1.6MiB live, 367.9MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 944×lower-*.f32
5 926×lower-*.f64
2 928×lower-/.f32
2 918×lower-/.f64
1 310×times-frac
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
029124
053112
1159108
2786108
37043108
08069108
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
21 → 948
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) n)
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
(/.f64 #s(literal 1 binary64) k)
(PI.f64)
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
(*.f64 n (PI.f64))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))) #s(literal 1/2 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) n)) (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) n)))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 (neg.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (neg.f64 (PI.f64)))) (sqrt.f64 (neg.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (neg.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(pow.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 (/.f64 n k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)) k)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)) 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 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) 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 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))))
(*.f64 (pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))) (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) n))
(pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (*.f64 #s(literal 2 binary64) n)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) n))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64)))
(*.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 n)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 n) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 #s(literal 2 binary64) n)
(*.f64 n #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) n))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))))
(sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(neg.f64 (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (PI.f64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (PI.f64)))))
(/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(/.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(/.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (neg.f64 k))) (sqrt.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (PI.f64) k)))) (sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) k)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (PI.f64)))) (neg.f64 (sqrt.f64 (neg.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 (PI.f64) k))) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))))
(/.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (PI.f64)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (PI.f64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))) #s(literal 1/4 binary64))
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(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) n) k)) (/.f64 (PI.f64) (*.f64 k (pow.f64 (PI.f64) k))))
(*.f64 (/.f64 (cbrt.f64 (PI.f64)) (*.f64 k (pow.f64 (PI.f64) k))) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) n) k)))
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(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) k))
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(*.f64 (/.f64 (neg.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (/.f64 (cbrt.f64 (PI.f64)) (neg.f64 k)))
(*.f64 (/.f64 (PI.f64) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 n k)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 n k)))
(*.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (/.f64 (/.f64 (cbrt.f64 (PI.f64)) k) (pow.f64 n k)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (/.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (pow.f64 n k)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) k)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k))))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)))) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)) k) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)) (PI.f64)) (/.f64 #s(literal 1 binary64) k))
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)) #s(literal 1 binary64)) (/.f64 (PI.f64) k))
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) k))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
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(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 n (cbrt.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 n (sqrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 n (cbrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 n (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 n (sqrt.f64 (PI.f64)))))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
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(*.f64 (*.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))

simplify603.0ms (5.2%)

Memory
11.5MiB live, 947.8MiB allocated
Algorithm
1×egg-herbie
Rules
19 914×lower-fma.f64
19 914×lower-fma.f32
6 144×lower-*.f64
6 144×lower-*.f32
3 716×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02152701
16212593
223492530
364792451
083582434
Stop Event
1×iter limit
1×node limit
Counts
300 → 300
Calls
Call 1
Inputs
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
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(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
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(* 2 n)
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(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(* 2 n)
(sqrt (/ (PI) k))
(/ (+ (sqrt (* k (PI))) (* -1/2 (* (sqrt (* (pow k 3) (PI))) (log (* 2 (* n (PI))))))) k)
(/ (+ (sqrt (* k (PI))) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (PI))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* -1/2 (* (sqrt (/ (PI) k)) (log (* 2 (* n (PI))))))))) k)
(/ (+ (sqrt (* k (PI))) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (PI) k)) (log (* 2 (* n (PI)))))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* -1/2 (* (sqrt (/ k (PI))) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* -1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (+ (* 1/6 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (* 1/4 (/ (* (PI) (pow (log (* 2 (* n (PI)))) 2)) k)))))))))))) k)
(sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k))))
(sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k))))
(sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k))))
(sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k))))
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(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (pow (sqrt -1) 2))
(* (sqrt (/ (PI) (* k (pow (* 2 (* n (PI))) k)))) (pow (sqrt -1) 2))
(sqrt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(sqrt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(sqrt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
(sqrt (/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))
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(sqrt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(sqrt (/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
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(sqrt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
(sqrt (/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))
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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))
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(sqrt k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
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(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
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(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
(sqrt (/ n k))
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(/ n k)
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
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(* (sqrt (* n (PI))) (sqrt 2))
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(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
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(sqrt (* n (PI)))
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(sqrt (* n (PI)))
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(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
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(/ 1 (pow k 2))
(/ 1 (pow k 2))
(/ 1 (pow k 2))
(/ 1 (pow k 2))
(/ 1 (pow k 2))
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(/ 1 (pow k 2))
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(/ 1 k)
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(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(* 2 (* n (PI)))
(/ (PI) k)
(/ (+ (PI) (* -1 (* k (* (PI) (log (* 2 (* n (PI)))))))) k)
(/ (+ (PI) (* k (- (* -1 (* k (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* (PI) (log (* 2 (* n (PI)))))))) k)
(/ (+ (PI) (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* -1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (* 1/6 (* (PI) (pow (log (* 2 (* n (PI)))) 3))))))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* (PI) (log (* 2 (* n (PI)))))))) k)
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(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
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(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
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(/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
Outputs
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
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(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) 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 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #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)
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(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 n k)))
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 n k)))
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 n k)))
(* (sqrt (/ n k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 n k)))
(/ n k)
(/.f64 n k)
(/ n k)
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(/ n k)
(/.f64 n k)
(/ n k)
(/.f64 n k)
(/ n k)
(/.f64 n k)
(/ n k)
(/.f64 n k)
(/ n k)
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(/ n k)
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(/ n k)
(/.f64 n k)
(/ n k)
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(/ n k)
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(/ n k)
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(/ n k)
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(/ n k)
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(/ n k)
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(/ n k)
(/.f64 n k)
(/ n k)
(/.f64 n k)
(/ n k)
(/.f64 n k)
(/ n k)
(/.f64 n k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* -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))))
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(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
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(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(* (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))) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(* -1 (* (sqrt (* n (PI))) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(/ 1 (pow k 2))
(/.f64 #s(literal 1 binary64) (*.f64 k k))
(/ 1 (pow k 2))
(/.f64 #s(literal 1 binary64) (*.f64 k k))
(/ 1 (pow k 2))
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(/ 1 (pow k 2))
(/.f64 #s(literal 1 binary64) (*.f64 k k))
(/ 1 (pow k 2))
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(/ 1 (pow k 2))
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(/ 1 (pow k 2))
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(/ 1 (pow k 2))
(/.f64 #s(literal 1 binary64) (*.f64 k k))
(/ 1 (pow k 2))
(/.f64 #s(literal 1 binary64) (*.f64 k k))
(/ 1 (pow k 2))
(/.f64 #s(literal 1 binary64) (*.f64 k k))
(/ 1 (pow k 2))
(/.f64 #s(literal 1 binary64) (*.f64 k k))
(/ 1 (pow k 2))
(/.f64 #s(literal 1 binary64) (*.f64 k 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 -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
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(/ 1 k)
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(/ 1 k)
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(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(/ 1 k)
(/.f64 #s(literal 1 binary64) k)
(* 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)))
(/ (PI) k)
(/.f64 (PI.f64) k)
(/ (+ (PI) (* -1 (* k (* (PI) (log (* 2 (* n (PI)))))))) k)
(/.f64 (fma.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (*.f64 (PI.f64) k)) (PI.f64)) k)
(/ (+ (PI) (* k (- (* -1 (* k (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* (PI) (log (* 2 (* n (PI)))))))) k)
(/.f64 (fma.f64 k (fma.f64 (*.f64 k (*.f64 (PI.f64) #s(literal 1/2 binary64))) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (PI.f64)))) (PI.f64)) k)
(/ (+ (PI) (* k (- (* k (- (* -1 (* k (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* -1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 3))) (* 1/6 (* (PI) (pow (log (* 2 (* n (PI)))) 3))))))) (+ (* -1 (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (* (PI) (log (* 2 (* n (PI)))))))) k)
(/.f64 (fma.f64 k (-.f64 (*.f64 k (fma.f64 k (*.f64 (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) #s(literal -1/6 binary64)) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))) (*.f64 (PI.f64) (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) (PI.f64)) k)
(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (pow (* 2 (* n (PI))) k)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))
(/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))
(/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))
(/ (PI) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) k)))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))
(* n (PI))
(*.f64 n (PI.f64))

eval237.0ms (2%)

Memory
22.5MiB live, 426.4MiB allocated
Compiler

Compiled 23 874 to 3 702 computations (84.5% saved)

prune259.0ms (2.2%)

Memory
-43.7MiB live, 407.6MiB allocated
Pruning

32 alts after pruning (24 fresh and 8 done)

PrunedKeptTotal
New1 530111 541
Fresh41317
Picked055
Done033
Total1 534321 566
Accuracy
100.0%
Counts
1 566 → 32
Alt Table
Click to see full alt table
StatusAccuracyProgram
14.1%
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k) #s(literal 1/4 binary64))
22.5%
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) (*.f64 k k))) #s(literal 1/8 binary64))
✓14.1%
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))
5.4%
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
14.9%
(pow.f64 (*.f64 k k) #s(literal -1/4 binary64))
5.4%
(pow.f64 k #s(literal -1/2 binary64))
✓99.4%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
56.7%
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
56.7%
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
✓56.9%
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k))
56.9%
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
57.0%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
5.4%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
46.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
✓5.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
79.2%
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
✓43.3%
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
57.0%
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
5.4%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))))
99.4%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
56.9%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓43.5%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
86.1%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
✓99.7%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
57.0%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
5.4%
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
57.0%
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
86.3%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
43.6%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
5.4%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
✓5.4%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
14.1%
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
Compiler

Compiled 1 188 to 494 computations (58.4% saved)

regimes101.0ms (0.9%)

Memory
21.2MiB live, 136.7MiB allocated
Counts
61 → 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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.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 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.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 (/.f64 (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (*.f64 k k) #s(literal -1/4 binary64))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) (*.f64 k k))) #s(literal 1/8 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 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 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (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))))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(*.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) (*.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 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
(*.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 (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 n (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 #s(literal 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 #s(literal 1 binary64) (sqrt.f64 k)) (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))))))
Outputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
Calls

4 calls:

47.0ms
(*.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))))
17.0ms
k
17.0ms
n
16.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
99.7%1k
99.7%1n
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes59.0ms (0.5%)

Memory
-17.7MiB live, 100.8MiB allocated
Counts
49 → 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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.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 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.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 (/.f64 (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (*.f64 k k) #s(literal -1/4 binary64))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) (*.f64 k k))) #s(literal 1/8 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 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 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) 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 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (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))))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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))))))
Outputs
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
Calls

4 calls:

16.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
14.0ms
n
13.0ms
k
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
99.4%1k
99.4%1n
99.4%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))))
99.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes49.0ms (0.4%)

Memory
13.0MiB live, 92.9MiB allocated
Counts
38 → 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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.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 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.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 (/.f64 (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (*.f64 k k) #s(literal -1/4 binary64))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) (*.f64 k k))) #s(literal 1/8 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 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 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) 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))
Outputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
Calls

4 calls:

13.0ms
k
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))))
11.0ms
n
10.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
98.4%2k
62.3%4n
98.4%3(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
62.3%4(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes22.0ms (0.2%)

Memory
13.3MiB live, 52.3MiB allocated
Counts
36 → 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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.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 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.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 (/.f64 (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (*.f64 k k) #s(literal -1/4 binary64))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) (*.f64 k k))) #s(literal 1/8 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/4 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
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) (*.f64 k k))) #s(literal 1/8 binary64))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
Calls

2 calls:

10.0ms
k
10.0ms
(*.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
75.5%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))))
75.5%2k
Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes22.0ms (0.2%)

Memory
-19.5MiB live, 57.4MiB allocated
Counts
33 → 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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.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 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.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 (/.f64 (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (*.f64 k k) #s(literal -1/4 binary64))
(sqrt.f64 (pow.f64 (*.f64 k k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) k) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) #s(literal -1/2 binary64))
Outputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(pow.f64 (*.f64 k k) #s(literal -1/4 binary64))
Calls

2 calls:

11.0ms
k
9.0ms
(*.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
67.3%2k
67.3%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)

regimes28.0ms (0.2%)

Memory
-34.1MiB live, 34.7MiB allocated
Counts
29 → 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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.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 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.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 (/.f64 (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 k))
(pow.f64 k #s(literal -1/2 binary64))
Outputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k))))
Calls

2 calls:

8.0ms
k
8.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
66.5%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))))
66.5%2k
Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes23.0ms (0.2%)

Memory
5.2MiB live, 43.9MiB allocated
Counts
16 → 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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
Outputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
Calls

4 calls:

7.0ms
n
5.0ms
k
5.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
5.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
57.0%1n
57.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
57.0%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))))
57.0%1k
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes11.0ms (0.1%)

Memory
22.5MiB live, 22.5MiB allocated
Counts
6 → 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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
Calls

4 calls:

3.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms
k
3.0ms
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))))
Results
AccuracySegmentsBranch
57.0%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))))
57.0%1n
57.0%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
57.0%1k
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes11.0ms (0.1%)

Memory
-18.9MiB live, 19.8MiB allocated
Counts
4 → 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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
Outputs
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
Calls

4 calls:

4.0ms
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))))
2.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Results
AccuracySegmentsBranch
43.6%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))))
43.6%1n
43.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
43.6%1k
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes8.0ms (0.1%)

Memory
22.6MiB live, 22.6MiB 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
k
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))))
Results
AccuracySegmentsBranch
5.4%1k
5.4%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))))
5.4%1n
5.4%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

bsearch25.0ms (0.2%)

Memory
3.4MiB live, 41.9MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
22.0ms
9.505096402145538e-7
76425.91566122767
Samples
16.0ms160×0valid
Compiler

Compiled 291 to 238 computations (18.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 3.0ms (27.6% of total)
ival-pow: 3.0ms (27.6% of total)
ival-div: 2.0ms (18.4% of total)
ival-pi: 1.0ms (9.2% of total)
ival-sub: 1.0ms (9.2% of total)
ival-sqrt: 1.0ms (9.2% 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
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1.2878952839219277e-115
Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch30.0ms (0.3%)

Memory
-24.2MiB live, 17.2MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
29.0ms
9.505096402145538e-7
76425.91566122767
Samples
7.0ms80×0valid
Compiler

Compiled 221 to 178 computations (19.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-pow: 2.0ms (37.5% of total)
ival-div: 1.0ms (18.8% of total)
ival-mult: 1.0ms (18.8% of total)
ival-sqrt: 1.0ms (18.8% of total)
ival-pi: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
2.2MiB live, 2.2MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
1.0ms
9.505096402145538e-7
76425.91566122767
Compiler

Compiled 261 to 198 computations (24.1% saved)

simplify8.0ms (0.1%)

Memory
14.8MiB live, 14.8MiB allocated
Algorithm
1×egg-herbie
Rules
22×*-commutative_binary64
4×+-commutative_binary64
4×sub-neg_binary64
2×1-exp_binary64
2×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058164
172164
276164
378164
479164
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) 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)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) (*.f64 k k))) #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
(if (<=.f64 k #s(literal 4458563631096791/9007199254740992 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (pow.f64 (*.f64 k k) #s(literal -1/4 binary64)))
(if (<=.f64 k #s(literal 4458563631096791/9007199254740992 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
Outputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (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 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))))
(if (<=.f64 k #s(literal 1 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (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)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) (*.f64 k k))) #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
(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)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 k k) (*.f64 k k))) #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
(if (<=.f64 k #s(literal 4458563631096791/9007199254740992 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (pow.f64 (*.f64 k k) #s(literal -1/4 binary64)))
(if (<=.f64 k #s(literal 4458563631096791/9007199254740992 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.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 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(sqrt.f64 (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))

soundness1.2s (9.9%)

Memory
7.4MiB live, 1 061.9MiB allocated
Rules
14 516×lower-fma.f64
14 516×lower-fma.f32
9 974×lower-fma.f64
9 974×lower-fma.f32
6 962×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029124
053112
1159108
2786108
37043108
08069108
03874873
112484677
241744404
080294241
01343
02243
18940
249738
3447438
0859937
029103
053101
1171100
292294
0831794
01281174
13451155
210111065
333481038
45547966
08354945
039174
070174
1250163
21521149
08343149
Stop Event
1×fuel
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
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 477 to 311 computations (34.8% saved)

preprocess103.0ms (0.9%)

Memory
13.1MiB live, 214.1MiB allocated
Compiler

Compiled 368 to 142 computations (61.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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