Migdal et al, Equation (51)

Time bar (total: 15.0s)

analyze148.0ms (1%)

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

Compiled 19 to 14 computations (26.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 95.0ms
ival-pow: 44.0ms (46.3% of total)
ival-mult: 21.0ms (22.1% of total)
ival-div: 13.0ms (13.7% of total)
ival-sqrt: 7.0ms (7.4% of total)
ival-sub: 5.0ms (5.3% of total)
ival-pi: 4.0ms (4.2% of total)
const: 1.0ms (1.1% of total)
backward-pass: 0.0ms (0% of total)

sample4.7s (31.4%)

Results
1.8s3932×5exit
1.0s8256×0valid
626.0ms1930×1invalid
36.0ms234×0unsamplable
34.0ms408×0invalid
Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-pow: 842.0ms (32.7% of total)
ival-mult: 510.0ms (19.8% of total)
ival-div: 495.0ms (19.3% of total)
backward-pass: 252.0ms (9.8% of total)
ival-sqrt: 221.0ms (8.6% of total)
ival-sub: 121.0ms (4.7% of total)
ival-pi: 94.0ms (3.7% of total)
const: 35.0ms (1.4% of total)
Bogosity

preprocess139.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
465×fma-define
240×fmm-def
123×associate-*r*
80×associate-*l*
74×sub-neg
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
039438
196380
2211380
3410364
4686352
51171352
61433352
71696352
82015352
92058352
102086352
112097352
122099352
Stop Event
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))))
(*.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64)))))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 (-.f64 #s(literal 1 binary64) n) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (/.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (neg.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 (neg.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal -2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal -2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (neg.f64 k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (neg.f64 k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (neg.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))) (neg.f64 (sqrt.f64 (neg.f64 k))))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal -2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal -2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 (-.f64 #s(literal 1 binary64) n) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (pow.f64 (*.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 n #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 n #s(literal 2 binary64)))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 n #s(literal -2 binary64)))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 n #s(literal -1/2 binary64)))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 n #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 n))

explain140.0ms (0.9%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
6216(2.381220319133451e+111 1.6520881937781154e-266)1(8.410668575811759e-8 3.097523168230435e+84)(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
00-0-(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
00-0-(PI.f64)
00-0-(*.f64 #s(literal 2 binary64) (PI.f64))
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
00-0-(-.f64 #s(literal 1 binary64) k)
00-0-#s(literal 2 binary64)
00-0-(sqrt.f64 k)
00-0-(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
00-0-#s(literal 1 binary64)
00-0-(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
00-0-n
00-0-k
Results
87.0ms512×0valid
Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 53.0ms
ival-pow: 20.0ms (38% of total)
ival-mult: 11.0ms (20.9% of total)
ival-div: 9.0ms (17.1% of total)
ival-sqrt: 5.0ms (9.5% of total)
ival-sub: 4.0ms (7.6% of total)
ival-pi: 3.0ms (5.7% of total)
const: 1.0ms (1.9% of total)
backward-pass: 0.0ms (0% of total)

eval1.0ms (0%)

Compiler

Compiled 59 to 23 computations (61% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.2%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶99.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 34 to 25 computations (26.5% saved)

localize136.0ms (0.9%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 k #s(literal 2 binary64))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
✓cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy100.0%
(PI.f64)
✓accuracy99.7%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.3%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.3%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
Rules
16×sub-neg
15×fma-define
13×*-commutative
8×+-commutative
6×associate-*r*
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
026359
145347
265347
386347
4106323
5129323
6156323
7184323
8192323
9193323
Stop Event
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))))
(/.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)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(/.f64 k #s(literal 2 binary64))
k
(sqrt.f64 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (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)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(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 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(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 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 k #s(literal 2 binary64))
k
(sqrt.f64 k)
Results
85.0ms256×0valid
Compiler

Compiled 105 to 21 computations (80% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-pow: 16.0ms (37.4% of total)
ival-mult: 11.0ms (25.7% of total)
ival-div: 9.0ms (21% of total)
ival-sub: 3.0ms (7% of total)
ival-sqrt: 2.0ms (4.7% of total)
ival-pi: 1.0ms (2.3% of total)
const: 1.0ms (2.3% of total)
backward-pass: 0.0ms (0% of total)

series89.0ms (0.6%)

Counts
12 → 160
Calls
Call 1
Inputs
#<alt (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))>
#<alt (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))>
#<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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))>
#<alt (*.f64 (PI.f64) n)>
#<alt (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))>
#<alt (PI.f64)>
#<alt (sqrt.f64 k)>
#<alt (*.f64 #s(literal 2 binary64) (PI.f64))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
#<alt (/.f64 k #s(literal 2 binary64))>
Outputs
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
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#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
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#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
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#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
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#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
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#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
Calls

42 calls:

TimeVariablePointExpression
35.0ms
n
@0
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
22.0ms
n
@-inf
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
7.0ms
n
@inf
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
3.0ms
k
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms
k
@0
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))

rewrite472.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
1096×log1p-expm1-u
523×expm1-log1p-u
292×prod-diff
148×add-exp-log
148×pow1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026274
1427270
24798270
Stop Event
1×node limit
Counts
12 → 299
Calls
Call 1
Inputs
(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 1 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 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(*.f64 (PI.f64) n)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(PI.f64)
(sqrt.f64 k)
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(/.f64 k #s(literal 2 binary64))
Outputs
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
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(*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k))
(*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k)))
(*.f64 (cbrt.f64 k) (/.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (/.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 k))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 k)))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 k) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 k))
(log.f64 (exp.f64 (sqrt.f64 k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 k))))
(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 k)))
(log1p.f64 (expm1.f64 (sqrt.f64 k)))
(exp.f64 (log.f64 (sqrt.f64 k)))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)) n))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 k #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) (cbrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) (*.f64 (cbrt.f64 k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) (/.f64 (cbrt.f64 k) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (neg.f64 k) #s(literal -1/2 binary64))
(pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64))
(neg.f64 (*.f64 k #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (sqrt.f64 (exp.f64 k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 k #s(literal 1/2 binary64)))))
(cbrt.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 k #s(literal 1/2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 k #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (*.f64 k #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64)))

simplify299.0ms (2%)

Algorithm
1×egg-herbie
Rules
724×fma-define
431×associate-*r*
366×associate-*l*
339×exp-prod
298×cube-prod
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
059819230
1121217176
2421516542
Stop Event
1×node limit
Counts
459 → 409
Calls
Call 1
Inputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
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(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (PI.f64))) #s(literal 1 binary64))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)))
(log.f64 (exp.f64 (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (PI.f64))))
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (PI.f64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 k))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k))
(*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k)))
(*.f64 (cbrt.f64 k) (/.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (/.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 k))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 k)))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 k) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 k))
(log.f64 (exp.f64 (sqrt.f64 k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 k))))
(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 k)))
(log1p.f64 (expm1.f64 (sqrt.f64 k)))
(exp.f64 (log.f64 (sqrt.f64 k)))
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)) n))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 k #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) (cbrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) (*.f64 (cbrt.f64 k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) (/.f64 (cbrt.f64 k) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (neg.f64 k) #s(literal -1/2 binary64))
(pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64))
(neg.f64 (*.f64 k #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (sqrt.f64 (exp.f64 k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 k #s(literal 1/2 binary64)))))
(cbrt.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 k #s(literal 1/2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 k #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (*.f64 k #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
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(expm1.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) k)))
(+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) (cbrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) k)) (cbrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 k #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) k)) (cbrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 k #s(literal 2 binary64)))))
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) (*.f64 (cbrt.f64 k) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) (/.f64 (cbrt.f64 k) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 (neg.f64 k) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 3 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(pow.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(pow.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(neg.f64 (*.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 k #s(literal 2 binary64))))
(fabs.f64 (*.f64 #s(literal 1/2 binary64) k))
(log.f64 (sqrt.f64 (exp.f64 k)))
(*.f64 #s(literal 1/2 binary64) k)
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1/2 binary64) k)
(cbrt.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(expm1.f64 (log1p.f64 (*.f64 k #s(literal 1/2 binary64))))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) k)))
(+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) k)
(exp.f64 (log.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) k)
(exp.f64 (*.f64 (log.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) k)

eval58.0ms (0.4%)

Compiler

Compiled 9611 to 1561 computations (83.8% saved)

prune76.0ms (0.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New44317460
Fresh000
Picked112
Done000
Total44418462
Accuracy
100.0%
Counts
462 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.9%
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
74.4%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
✓99.2%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
96.1%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
99.1%
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
▶99.3%
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
▶99.3%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
▶95.8%
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
99.1%
(/.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))))))
▶99.2%
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
76.2%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
48.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
76.0%
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
39.1%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
99.2%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
39.1%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
▶39.1%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
38.2%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
Compiler

Compiled 612 to 444 computations (27.5% saved)

localize584.0ms (3.9%)

Algorithm
1×egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
✓cost-diff0
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓cost-diff0
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
✓cost-diff384
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
✓cost-diff0
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
✓cost-diff192
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
✓cost-diff192
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
✓cost-diff0
(-.f64 #s(literal 1 binary64) k)
cost-diff0
(PI.f64)
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
✓cost-diff0
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓cost-diff0
(*.f64 n (/.f64 (PI.f64) k))
✓cost-diff0
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓cost-diff0
(pow.f64 k #s(literal -1/2 binary64))
✓cost-diff0
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓cost-diff384
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
✓accuracy99.6%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy99.6%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))
✓accuracy99.4%
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
accuracy78.1%
(PI.f64)
✓accuracy99.6%
(*.f64 n (PI.f64))
✓accuracy99.6%
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
✓accuracy96.2%
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
accuracy78.1%
(PI.f64)
✓accuracy99.7%
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
✓accuracy99.6%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy99.3%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
accuracy78.1%
(PI.f64)
✓accuracy99.7%
(/.f64 (PI.f64) k)
✓accuracy99.4%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
✓accuracy90.3%
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
accuracy78.1%
(PI.f64)
✓accuracy99.6%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
✓accuracy99.6%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓accuracy99.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
accuracy78.1%
(PI.f64)
Rules
1285×fma-define
472×div-sub
326×fmm-def
304×times-frac
245×distribute-lft-neg-out
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
045977
185977
2115949
3188949
4355893
5607893
6903893
71403893
82320893
92832893
103357893
113503893
123729893
134170893
144731893
155515893
167697893
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 k #s(literal -1/2 binary64))
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
(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 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (/.f64 (PI.f64) k))
n
(/.f64 (PI.f64) k)
(PI.f64)
k
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
n
(PI.f64)
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) k)
k
(sqrt.f64 k)
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(sqrt.f64 k)
k
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
Outputs
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 k #s(literal -1/2 binary64))
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
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)
(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (PI.f64) (/.f64 k n))
n
(/.f64 (PI.f64) k)
(PI.f64)
k
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (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))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 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 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
n
(PI.f64)
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
k
(sqrt.f64 k)
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (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))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(*.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 k) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(sqrt.f64 k)
k
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.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)))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)
(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
Results
180.0ms198×0valid
124.0ms58×5exit
Compiler

Compiled 283 to 40 computations (85.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 127.0ms
ival-pow: 40.0ms (31.5% of total)
ival-mult: 30.0ms (23.6% of total)
backward-pass: 23.0ms (18.1% of total)
ival-sqrt: 12.0ms (9.4% of total)
ival-div: 9.0ms (7.1% of total)
ival-log: 5.0ms (3.9% of total)
ival-sub: 3.0ms (2.4% of total)
ival-exp: 2.0ms (1.6% of total)
const: 1.0ms (0.8% of total)
ival-pi: 1.0ms (0.8% of total)

series53.0ms (0.4%)

Counts
22 → 356
Calls
Call 1
Inputs
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))>
#<alt (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))>
#<alt (/.f64 (PI.f64) k)>
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))>
#<alt (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))>
#<alt (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))>
#<alt (*.f64 n (PI.f64))>
#<alt (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))>
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))>
#<alt (/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))>
#<alt (pow.f64 k #s(literal -1/2 binary64))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (*.f64 n (/.f64 (PI.f64) k))>
#<alt (-.f64 #s(literal 1 binary64) k)>
#<alt (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))>
Outputs
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))>
#<alt #s(literal 1 binary64)>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 k (+.f64 (*.f64 #s(literal 1/48 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
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#<alt (/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (+.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/48 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
Calls

99 calls:

TimeVariablePointExpression
3.0ms
k
@-inf
(/ (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))) (sqrt k))
3.0ms
n
@inf
(* (pow (* n (* 2 (PI))) (* 1/2 (- 1 k))) (pow k -1/2))
2.0ms
k
@0
(/ (* (pow k -1/2) (sqrt (* 2 (* (PI) n)))) (pow (* 2 (* (PI) n)) (* k 1/2)))
1.0ms
k
@-inf
(/ (sqrt (* n (* 2 (PI)))) (* (sqrt k) (pow (* n (* 2 (PI))) (* 1/2 k))))
1.0ms
n
@-inf
(/ (* (pow k -1/2) (sqrt (* 2 (* (PI) n)))) (pow (* 2 (* (PI) n)) (* k 1/2)))

rewrite279.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
309×log1p-expm1-u
309×expm1-log1p-u
299×add-cube-cbrt
298×add-exp-log
298×pow1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
045609
1823585
Stop Event
1×node limit
Counts
22 → 776
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(/.f64 (PI.f64) k)
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 n (PI.f64))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(pow.f64 k #s(literal -1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(-.f64 #s(literal 1 binary64) k)
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64)))) (sqrt.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))) #s(literal 1 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(exp.f64 (log.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k))
(*.f64 (pow.f64 (sqrt.f64 n) k) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (sqrt.f64 n) k))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) (*.f64 k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 k #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (*.f64 k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (*.f64 k #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) k) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) k) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) k))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(log.f64 (exp.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))))
(cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(exp.f64 (*.f64 k (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(exp.f64 (*.f64 (*.f64 k (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) k))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/2 binary64)))
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(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
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(*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64))) (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))) (/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 1 binary64)))

simplify602.0ms (4%)

Algorithm
1×egg-herbie
Rules
724×associate-*l*
338×associate-/l*
288×*-commutative
284×times-frac
263×associate-*l/
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0120461507
1261256890
Stop Event
1×node limit
Counts
1132 → 837
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
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#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
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(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
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(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
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(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
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(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
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(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
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#s(literal 1 binary64)
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(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal -1 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 1 binary64)))
Outputs
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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eval147.0ms (1%)

Compiler

Compiled 23841 to 3767 computations (84.2% saved)

prune173.0ms (1.2%)

Pruning

17 alts after pruning (14 fresh and 3 done)

PrunedKeptTotal
New1084101094
Fresh8412
Picked325
Done011
Total1095171112
Accuracy
100.0%
Counts
1112 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.2%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
99.1%
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
48.3%
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
76.5%
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
98.9%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
76.2%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))
✓95.8%
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
▶99.1%
(/.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))))))
▶75.9%
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
76.0%
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
▶39.1%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶48.6%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
✓39.1%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
89.8%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
38.8%
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
38.8%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶38.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
Compiler

Compiled 489 to 353 computations (27.8% saved)

localize336.0ms (2.2%)

Algorithm
1×egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff0
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
✓cost-diff0
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))
✓cost-diff0
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
✓cost-diff0
(sqrt.f64 (/.f64 (PI.f64) k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
cost-diff0
(*.f64 n (PI.f64))
✓cost-diff0
(/.f64 (*.f64 n (PI.f64)) k)
✓cost-diff0
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (/.f64 n k))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
cost-diff0
(sqrt.f64 k)
✓accuracy99.6%
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))
✓accuracy99.6%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
✓accuracy90.0%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
accuracy51.9%
(PI.f64)
accuracy99.8%
(/.f64 (PI.f64) k)
✓accuracy99.7%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
✓accuracy99.6%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
accuracy51.9%
(PI.f64)
accuracy99.7%
(*.f64 n (PI.f64))
✓accuracy99.6%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy90.4%
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
accuracy51.9%
(PI.f64)
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
✓accuracy99.8%
(*.f64 (PI.f64) (/.f64 n k))
✓accuracy90.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
accuracy51.9%
(PI.f64)
accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy99.7%
(/.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)))))
✓accuracy99.3%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
accuracy51.9%
(PI.f64)
Rules
32×*-commutative
24×fma-define
16×associate-*r*
15×sub-neg
14×associate-*l*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040792
168792
2110770
3153770
4189770
5217770
6249770
7276770
8282770
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.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))))))
#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 k)
k
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 k #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
#s(literal 2 binary64)
(*.f64 (PI.f64) (/.f64 n k))
(PI.f64)
(/.f64 n k)
n
k
(*.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 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(PI.f64)
k
(sqrt.f64 n)
n
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
#s(literal -1/2 binary64)
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 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))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 k)
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))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 k #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k)))
#s(literal 2 binary64)
(*.f64 (PI.f64) (/.f64 n k))
(PI.f64)
(/.f64 n k)
n
k
(*.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 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(PI.f64)
k
(sqrt.f64 n)
n
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k)))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
#s(literal -1/2 binary64)
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k)))
Results
157.0ms69×5exit
56.0ms129×0valid
27.0ms58×0unsamplable
Compiler

Compiled 218 to 35 computations (83.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 113.0ms
ival-pow: 36.0ms (31.8% of total)
ival-mult: 21.0ms (18.5% of total)
backward-pass: 19.0ms (16.8% of total)
ival-sqrt: 18.0ms (15.9% of total)
ival-div: 16.0ms (14.1% of total)
ival-sub: 2.0ms (1.8% of total)
const: 1.0ms (0.9% of total)
ival-pi: 1.0ms (0.9% of total)

series52.0ms (0.3%)

Counts
16 → 296
Calls
Call 1
Inputs
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))>
#<alt (/.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)))))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))>
#<alt (*.f64 (PI.f64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))>
#<alt (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)>
#<alt (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (sqrt.f64 (/.f64 (PI.f64) k))>
#<alt (*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))>
Outputs
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
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#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))) k)>
#<alt (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) k))))))))))))) k)>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
Calls

90 calls:

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

rewrite318.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
275×associate-*r*
252×log1p-expm1-u
252×expm1-log1p-u
244×prod-diff
241×pow1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
038497
1671480
27888480
Stop Event
1×node limit
Counts
16 → 561
Calls
Call 1
Inputs
(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 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 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(/.f64 (*.f64 n (PI.f64)) k)
(sqrt.f64 (/.f64 (PI.f64) k))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
Outputs
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(*.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))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(*.f64 (pow.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
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(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) #s(literal 1 binary64))
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(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))) #s(literal 1 binary64)))
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simplify716.0ms (4.8%)

Algorithm
1×egg-herbie
Rules
330×exp-prod
311×*-commutative
278×fma-define
253×cube-prod
219×associate-*r/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0108737182
1246134121
2633733297
Stop Event
1×node limit
Counts
857 → 680
Calls
Call 1
Inputs
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (pow.f64 k #s(literal 3 binary64))) (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (+.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))))))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
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(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))) (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (/.f64 (PI.f64) k)) n))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (*.f64 (PI.f64) n)) k))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (pow.f64 n #s(literal 2 binary64))) (*.f64 (cbrt.f64 n) (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 (/.f64 n k)) (*.f64 (sqrt.f64 (/.f64 n k)) (PI.f64)))
(*.f64 (*.f64 (PI.f64) (neg.f64 n)) (/.f64 #s(literal 1 binary64) (neg.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 (PI.f64) n))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (PI.f64) n) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (*.f64 (PI.f64) n) (cbrt.f64 k)))
(*.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))
(*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (/.f64 n (sqrt.f64 k)))
(*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 n k))
(*.f64 (/.f64 (PI.f64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 n (cbrt.f64 k)))
(*.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 (PI.f64) k))
(*.f64 (/.f64 n (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (PI.f64) (cbrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 (PI.f64) n)) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 k)))
(*.f64 (*.f64 (/.f64 (PI.f64) k) (sqrt.f64 n)) (sqrt.f64 n))
(*.f64 (*.f64 (/.f64 (PI.f64) k) (cbrt.f64 (pow.f64 n #s(literal 2 binary64)))) (cbrt.f64 n))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 n k)) #s(literal 2 binary64))) (cbrt.f64 (/.f64 n k)))
(*.f64 (*.f64 (PI.f64) (sqrt.f64 (/.f64 n k))) (sqrt.f64 (/.f64 n k)))
(*.f64 (*.f64 n (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64))) (cbrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (*.f64 (/.f64 n k) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1 binary64))
(neg.f64 (/.f64 (*.f64 (PI.f64) n) (neg.f64 k)))
(neg.f64 (/.f64 (*.f64 (PI.f64) (neg.f64 n)) k))
(sqrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 (/.f64 n k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 n k) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k))))
(exp.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64)))
(exp.f64 (+.f64 (log.f64 (/.f64 (PI.f64) k)) (log.f64 n)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (PI.f64) k)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))) (cbrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (cbrt.f64 (/.f64 (PI.f64) k)) (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (/.f64 (PI.f64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (PI.f64) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (/.f64 (PI.f64) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) k)))))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)))) #s(literal 1 binary64))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) #s(literal 2 binary64)))
(log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))) #s(literal 1 binary64)))
(exp.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (log.f64 (sqrt.f64 k))))
Outputs
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 n (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 n (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 n (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 n (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 n (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
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(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)))
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eval193.0ms (1.3%)

Compiler

Compiled 18956 to 3533 computations (81.4% saved)

prune222.0ms (1.5%)

Pruning

28 alts after pruning (23 fresh and 5 done)

PrunedKeptTotal
New984211005
Fresh729
Picked235
Done123
Total994281022
Accuracy
100.0%
Counts
1022 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
28.2%
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
✓99.2%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶48.3%
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
✓99.1%
(/.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))))))
▶48.2%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
▶99.1%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
99.1%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))))
39.8%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
39.8%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
76.2%
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
48.6%
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
89.8%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
✓39.1%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
48.3%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
48.6%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
38.9%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
✓39.1%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
89.8%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
▶38.8%
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
38.8%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
38.8%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
38.8%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
38.8%
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
▶38.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
✓38.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
36.4%
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/2 binary64)))
29.9%
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)))
29.9%
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))) #s(literal 3/2 binary64)))
Compiler

Compiled 660 to 528 computations (20% saved)

localize426.0ms (2.8%)

Algorithm
1×egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
✓cost-diff0
(*.f64 n #s(literal 2 binary64))
✓cost-diff0
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
✓cost-diff0
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
✓cost-diff0
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
cost-diff0
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓cost-diff0
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
✓cost-diff0
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
✓cost-diff0
(/.f64 k (PI.f64))
✓cost-diff0
(/.f64 n (/.f64 k (PI.f64)))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
✓cost-diff0
(*.f64 k #s(literal -1/2 binary64))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
cost-diff0
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
accuracy99.6%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy99.6%
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓accuracy99.4%
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
accuracy78.1%
(PI.f64)
✓accuracy99.6%
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
✓accuracy99.6%
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
✓accuracy99.4%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
accuracy78.1%
(PI.f64)
✓accuracy99.8%
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
accuracy99.6%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy90.0%
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
accuracy78.1%
(PI.f64)
✓accuracy99.7%
(/.f64 n (/.f64 k (PI.f64)))
✓accuracy99.7%
(/.f64 k (PI.f64))
✓accuracy90.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
accuracy78.1%
(PI.f64)
✓accuracy99.7%
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k))
accuracy99.6%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy99.3%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
accuracy78.1%
(PI.f64)
Rules
22×*-commutative
19×fma-define
14×associate-/l*
14×sub-neg
14×associate-*l*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
035702
165682
2114666
3157666
4186666
5215666
6244666
7269666
8286666
9294666
10295666
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
#s(literal 1 binary64)
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(neg.f64 (+.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)))
#s(literal 1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 k)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
#s(literal 2 binary64)
(/.f64 n (/.f64 k (PI.f64)))
n
(/.f64 k (PI.f64))
k
(PI.f64)
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
k
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(PI.f64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 k)
k
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
Outputs
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k)))
#s(literal 1 binary64)
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 k #s(literal -1/2 binary64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(+.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 k #s(literal -1/2 binary64))))
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 k)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
#s(literal 2 binary64)
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
n
(/.f64 k (PI.f64))
k
(PI.f64)
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
(*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
k
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(PI.f64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.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 k))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 k)
k
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
Results
112.0ms198×0valid
18.0ms58×0unsamplable
Compiler

Compiled 202 to 30 computations (85.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 91.0ms
ival-div: 55.0ms (60.4% of total)
ival-mult: 12.0ms (13.2% of total)
ival-sqrt: 10.0ms (11% of total)
ival-pow: 10.0ms (11% of total)
ival-pi: 1.0ms (1.1% of total)
ival-add: 1.0ms (1.1% of total)
const: 1.0ms (1.1% of total)
ival-neg: 1.0ms (1.1% of total)
backward-pass: 0.0ms (0% of total)

series32.0ms (0.2%)

Counts
16 → 300
Calls
Call 1
Inputs
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))>
#<alt (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))>
#<alt (/.f64 k (PI.f64))>
#<alt (/.f64 n (/.f64 k (PI.f64)))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))>
#<alt (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)>
#<alt (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))>
#<alt (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))>
#<alt (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))>
#<alt (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))>
#<alt (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))>
#<alt (*.f64 k #s(literal -1/2 binary64))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))>
#<alt (*.f64 n #s(literal 2 binary64))>
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))>
Outputs
#<alt (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))>
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#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
Calls

78 calls:

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

rewrite281.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
427×log1p-expm1-u
234×prod-diff
222×associate-*r*
210×expm1-log1p-u
209×pow1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
034423
1571407
27147407
Stop Event
1×node limit
Counts
16 → 730
Calls
Call 1
Inputs
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(/.f64 k (PI.f64))
(/.f64 n (/.f64 k (PI.f64)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 k #s(literal -1/2 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
(*.f64 n #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
Outputs
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 n (*.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 n (*.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 (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))))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (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))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n #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 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.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 #s(literal -1 binary64) (neg.f64 (pow.f64 (*.f64 n (*.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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 2 binary64))
(sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 k #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(exp.f64 (log.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))) (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(*.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 n) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))))
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(/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64)) k)
(/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 k))
(pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -2 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1 binary64))
(neg.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 k)))
(neg.f64 (/.f64 (*.f64 n (neg.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 k (PI.f64)) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(exp.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64))
(sqrt.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) #s(literal 4 binary64)))
(log.f64 (pow.f64 (exp.f64 n) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n #s(literal 2 binary64)))))
(cbrt.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 n #s(literal 2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 n #s(literal 2 binary64))))
(exp.f64 (log.f64 (*.f64 n #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))) (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(*.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 n) (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(fabs.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))

simplify526.0ms (3.5%)

Algorithm
1×egg-herbie
Rules
565×times-frac
552×fma-define
481×exp-prod
382×associate-*r/
318×associate-*l/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0105038979
1231138246
2687138208
Stop Event
1×node limit
Counts
1030 → 680
Calls
Call 1
Inputs
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
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(*.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(fabs.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))
Outputs
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (neg.f64 (*.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(pow.f64 (exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (neg.f64 (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 k (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
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(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))
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(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
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(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (/.f64 #s(literal 1 binary64) (cbrt.f64 (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))))
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(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))
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(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 2 binary64)))) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (sqrt.f64 n) (/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
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(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
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(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)))
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(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (/.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (/.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 n) (/.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))) (neg.f64 (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 k))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1 binary64))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))) #s(literal 3 binary64))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(fabs.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))))))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))) #s(literal 1 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))

eval189.0ms (1.3%)

Compiler

Compiled 15754 to 3225 computations (79.5% saved)

prune368.0ms (2.5%)

Pruning

38 alts after pruning (30 fresh and 8 done)

PrunedKeptTotal
New982181000
Fresh61218
Picked145
Done145
Total990381028
Accuracy
100.0%
Counts
1028 → 38
Alt Table
Click to see full alt table
StatusAccuracyProgram
28.2%
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
28.2%
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
38.7%
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
39.9%
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
39.9%
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
✓99.2%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
48.3%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
✓48.3%
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
48.6%
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
38.7%
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal -1/2 binary64)))
48.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
✓99.1%
(/.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))))))
✓48.2%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
39.8%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))
39.8%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
76.2%
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
48.3%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
89.8%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
✓39.1%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
48.3%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
38.9%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
48.6%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
89.8%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
✓38.8%
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
38.8%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
38.8%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
38.8%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
38.1%
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
38.8%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
38.8%
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
38.8%
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
✓38.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
✓38.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
36.4%
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
29.9%
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)))
29.9%
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))) #s(literal 3/2 binary64)))
29.9%
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
29.9%
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
Compiler

Compiled 1305 to 608 computations (53.4% saved)

regimes85.0ms (0.6%)

Counts
68 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
Outputs
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
Calls

4 calls:

20.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
19.0ms
n
19.0ms
k
18.0ms
(*.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
99.3%1k
99.3%1n
99.3%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))))
99.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes79.0ms (0.5%)

Counts
66 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
Outputs
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
Calls

4 calls:

19.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms
k
18.0ms
n
17.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.3%1k
99.3%1n
99.3%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))))
99.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes127.0ms (0.9%)

Counts
62 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
Outputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Calls

4 calls:

68.0ms
k
21.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms
n
16.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.2%1k
99.2%1n
99.2%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.2%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes29.0ms (0.2%)

Counts
43 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
Outputs
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
Calls

2 calls:

13.0ms
k
12.0ms
n
Results
AccuracySegmentsBranch
99.6%2k
89.8%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes28.0ms (0.2%)

Counts
41 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
Outputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
Calls

2 calls:

12.0ms
n
12.0ms
k
Results
AccuracySegmentsBranch
55.9%3n
59.4%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes23.0ms (0.2%)

Counts
32 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1/2 binary64)))
Outputs
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
Calls

2 calls:

10.0ms
k
10.0ms
n
Results
AccuracySegmentsBranch
48.6%1n
48.6%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes15.0ms (0.1%)

Counts
21 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
Calls

2 calls:

7.0ms
k
6.0ms
n
Results
AccuracySegmentsBranch
48.6%1k
48.6%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

Counts
19 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) k) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
Outputs
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
Calls

2 calls:

6.0ms
k
6.0ms
n
Results
AccuracySegmentsBranch
39.9%1k
39.9%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Counts
10 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
Calls

2 calls:

4.0ms
n
3.0ms
k
Results
AccuracySegmentsBranch
38.8%1k
38.8%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

2 calls:

3.0ms
n
1.0ms
k
Results
AccuracySegmentsBranch
38.8%1k
38.8%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch17.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
15.0ms
1.5496883972140314e-66
9.149209381999714e-61
Results
11.0ms96×0valid
Compiler

Compiled 185 to 149 computations (19.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-div: 2.0ms (25.1% of total)
ival-mult: 2.0ms (25.1% of total)
ival-pow: 2.0ms (25.1% of total)
ival-sub: 1.0ms (12.5% of total)
ival-sqrt: 1.0ms (12.5% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch21.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
19.0ms
9.793824512200758e+19
1.8557828845981598e+21
Results
14.0ms112×0valid
Compiler

Compiled 205 to 171 computations (16.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-pow: 5.0ms (47.1% of total)
ival-div: 2.0ms (18.9% of total)
ival-mult: 2.0ms (18.9% of total)
ival-sub: 1.0ms (9.4% of total)
ival-sqrt: 1.0ms (9.4% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify12.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
19×*-commutative
6×+-commutative
5×sub-neg
3×1-exp
3×neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075544
1101544
2110544
3116544
4120544
5121544
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 8684406692798715/14474011154664524427946373126085988481658748083205070504932198000989141204992 binary64)) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 1850000000000000000000 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
Outputs
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 8684406692798715/14474011154664524427946373126085988481658748083205070504932198000989141204992 binary64)) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 8684406692798715/14474011154664524427946373126085988481658748083205070504932198000989141204992 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 1850000000000000000000 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))

soundness2.6s (17.3%)

Rules
1096×log1p-expm1-u
724×associate-*l*
724×fma-define
565×times-frac
552×fma-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
059819230
1121217176
2421516542
026274
1427270
24798270
0120461507
1261256890
045609
1823585
0105038979
1231138246
2687138208
034423
1571407
27147407
038497
1671480
27888480
039438
196380
2211380
3410364
4686352
51171352
61433352
71696352
82015352
92058352
102086352
112097352
122099352
Stop Event
1×fuel
1×saturated
1×node limit
1×node limit
1×node limit
1×node limit
1×node limit
1×node limit
1×node limit
Compiler

Compiled 2524 to 741 computations (70.6% saved)

preprocess164.0ms (1.1%)

Compiler

Compiled 330 to 154 computations (53.3% saved)

end2.0ms (0%)

Profiling

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