Migdal et al, Equation (51)

Time bar (total: 14.4s)

analyze194.0ms (1.3%)

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: 143.0ms
ival-pow: 94.0ms (65.7% of total)
ival-mult: 17.0ms (11.9% of total)
ival-div: 15.0ms (10.5% of total)
ival-sqrt: 8.0ms (5.6% of total)
ival-sub: 4.0ms (2.8% of total)
ival-pi: 3.0ms (2.1% of total)
const: 1.0ms (0.7% of total)
backward-pass: 0.0ms (0% of total)

sample5.3s (36.4%)

Results
2.0s3790×5exit
1.3s8256×0valid
508.0ms1908×1invalid
38.0ms421×0invalid
28.0ms184×0unsamplable
Precisions
Click to see histograms. Total time spent on operations: 3.0s
ival-pow: 861.0ms (28.6% of total)
ival-mult: 640.0ms (21.3% of total)
backward-pass: 487.0ms (16.2% of total)
ival-sub: 341.0ms (11.3% of total)
ival-div: 324.0ms (10.8% of total)
ival-sqrt: 235.0ms (7.8% of total)
ival-pi: 85.0ms (2.8% of total)
const: 36.0ms (1.2% of total)
Bogosity

preprocess181.0ms (1.3%)

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

Useful iterations: 4 (0.0ms)

IterNodesCost
039438
196380
2211380
3410364
4686352
51171352
61433352
71698352
82017352
92060352
102088352
112099352
122101352
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))

explain265.0ms (1.8%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
8213(3.106925941139245e+43 4.513130216943388e+136)0-(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
00-0-(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
00-0-(PI.f64)
00-0-(*.f64 #s(literal 2 binary64) (PI.f64))
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
00-0-(-.f64 #s(literal 1 binary64) k)
00-0-#s(literal 2 binary64)
00-0-(sqrt.f64 k)
00-0-(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
00-0-#s(literal 1 binary64)
00-0-(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
00-0-n
00-0-k
Results
80.0ms512×0valid
Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-pow: 18.0ms (37.8% of total)
ival-mult: 12.0ms (25.2% of total)
ival-div: 7.0ms (14.7% of total)
ival-sqrt: 4.0ms (8.4% of total)
ival-sub: 3.0ms (6.3% of total)
ival-pi: 2.0ms (4.2% of total)
const: 1.0ms (2.1% of total)
backward-pass: 0.0ms (0% of total)

eval1.0ms (0%)

Compiler

Compiled 59 to 23 computations (61% saved)

prune2.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.8%
(/.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))
▶98.7%
(*.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))))
Compiler

Compiled 34 to 25 computations (26.5% saved)

localize240.0ms (1.7%)

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))
✓accuracy99.7%
(*.f64 (PI.f64) n)
✓accuracy98.9%
(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))))
✓accuracy99.7%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy98.9%
(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
193.0ms256×0valid
Compiler

Compiled 105 to 21 computations (80% saved)

Precisions
Click to see histograms. Total time spent on operations: 168.0ms
ival-div: 127.0ms (75.8% of total)
ival-pow: 18.0ms (10.7% of total)
ival-mult: 16.0ms (9.6% of total)
ival-sub: 3.0ms (1.8% of total)
ival-sqrt: 2.0ms (1.2% of total)
ival-pi: 1.0ms (0.6% of total)
const: 1.0ms (0.6% of total)
backward-pass: 0.0ms (0% of total)

series305.0ms (2.1%)

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 #s(literal 1 binary64) (sqrt.f64 k))>
#<alt (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)>
#<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 (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 #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 (*.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 (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 (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 (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 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))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
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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 #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)>
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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)))))>
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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 -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
239.0ms
n
@0
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
23.0ms
n
@-inf
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
9.0ms
n
@inf
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
5.0ms
k
@0
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
1.0ms
k
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite412.0ms (2.9%)

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 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.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)))

simplify362.0ms (2.5%)

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)))))
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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)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
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(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
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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)

eval63.0ms (0.4%)

Compiler

Compiled 9611 to 1559 computations (83.8% saved)

prune237.0ms (1.6%)

Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New43822460
Fresh000
Picked112
Done000
Total43923462
Accuracy
100.0%
Counts
462 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.5%
(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))
98.7%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶73.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
98.7%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
▶98.7%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓98.8%
(/.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))
95.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
98.6%
(/.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))))
95.4%
(/.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))
98.8%
(/.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))))))
▶98.8%
(*.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)))
69.6%
(*.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)))
69.6%
(*.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)))) (pow.f64 k #s(literal -1/2 binary64))))
57.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (*.f64 k (*.f64 k (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))))
46.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
95.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 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)))))
69.5%
(*.f64 (*.f64 (pow.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))))) (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
35.8%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
95.4%
(*.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)))))
▶98.5%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
35.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
▶35.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
35.4%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
Compiler

Compiled 876 to 626 computations (28.5% saved)

localize447.0ms (3.1%)

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-diff0
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff64
(pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
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 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
(-.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)))
✓accuracy99.7%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
✓accuracy99.2%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))
✓accuracy99.1%
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
accuracy71.6%
(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)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
accuracy98.9%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓accuracy77.0%
(pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
accuracy71.6%
(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)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
accuracy98.9%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
accuracy71.6%
(PI.f64)
✓accuracy99.7%
(/.f64 (PI.f64) k)
✓accuracy99.5%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
✓accuracy88.5%
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
accuracy71.6%
(PI.f64)
✓accuracy99.8%
(*.f64 n (*.f64 #s(literal 2 binary64) (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)))
✓accuracy98.9%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
accuracy71.6%
(PI.f64)
Rules
29×fma-define
22×*-commutative
22×sub-neg
9×associate-+l-
9×+-commutative
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
042902
171902
299902
3130866
4161866
5201866
6254866
7293866
8301866
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.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 (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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
(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
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
#s(literal 1 binary64)
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(*.f64 #s(literal 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
(pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 k #s(literal 3/2 binary64))
#s(literal 3/2 binary64)
#s(literal 1/3 binary64)
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) 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 (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) k)))
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(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 (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 (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 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #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))))
(*.f64 (pow.f64 k #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))))
(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 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)))
(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 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))
(+.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))
(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 (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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 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 (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 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #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))))
(*.f64 (pow.f64 k #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))))
(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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(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)))
(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 2 binary64) (*.f64 (PI.f64) n))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(+.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))
(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
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
#s(literal 1 binary64)
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 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))) (cbrt.f64 (pow.f64 k #s(literal 3/2 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))) (cbrt.f64 (pow.f64 k #s(literal 3/2 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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(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)))
(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 2 binary64) (*.f64 (PI.f64) n))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(+.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))
(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
(pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
(pow.f64 k #s(literal 3/2 binary64))
#s(literal 3/2 binary64)
#s(literal 1/3 binary64)
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) 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 (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) k)))
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(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)
Results
173.0ms181×0valid
165.0ms74×5exit
0.0ms1×0invalid
Compiler

Compiled 270 to 37 computations (86.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 211.0ms
ival-sqrt: 77.0ms (36.5% of total)
ival-pow: 65.0ms (30.8% of total)
backward-pass: 27.0ms (12.8% of total)
ival-mult: 22.0ms (10.4% of total)
ival-div: 14.0ms (6.6% of total)
ival-sub: 3.0ms (1.4% of total)
ival-pi: 2.0ms (0.9% of total)
const: 1.0ms (0.5% of total)

series289.0ms (2%)

Counts
17 → 288
Calls
Call 1
Inputs
#<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 (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 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))>
#<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 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))>
#<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)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))>
#<alt (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))>
#<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)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))>
#<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 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (-.f64 #s(literal 1 binary64) k)>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (*.f64 n (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
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 (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 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
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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 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (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 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (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 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (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 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (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 #s(literal 1 binary64)>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))>
#<alt (*.f64 #s(literal -1 binary64) k)>
#<alt (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))>
#<alt (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))>
#<alt (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) k)>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.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)))>
Calls

75 calls:

TimeVariablePointExpression
234.0ms
n
@inf
(* (sqrt (* n (* 2 (PI)))) (/ (pow k -1/2) (pow (* n (* 2 (PI))) (* 1/2 k))))
3.0ms
k
@-inf
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (pow (pow k 3/2) 1/3))
2.0ms
n
@0
(sqrt (* n (/ (PI) k)))
2.0ms
k
@0
(pow (pow k 3/2) 1/3)
2.0ms
k
@-inf
(pow (pow k 3/2) 1/3)

rewrite155.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
284×log1p-expm1-u
284×expm1-log1p-u
283×associate-*r*
276×pow1
270×add-cube-cbrt
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
042479
1706453
Stop Event
1×node limit
Counts
17 → 446
Calls
Call 1
Inputs
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) 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 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(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)
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
(pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 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)))
(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 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(-.f64 #s(literal 1 binary64) k)
(sqrt.f64 #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
Outputs
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #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 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (+.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 (sqrt.f64 n) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 n) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))))
(*.f64 (pow.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.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 (sqrt.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 (cbrt.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)))) (pow.f64 (cbrt.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 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (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 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 n) k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/4 binary64) k))) (/.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 1/4 binary64) k))))
(*.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))))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (sqrt.f64 n) k)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/4 binary64) k))) (/.f64 (cbrt.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 1/4 binary64) k))))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 n) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/4 binary64) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/4 binary64) k))))
(*.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)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 n) k)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
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(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #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))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)))

simplify367.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
717×associate-*r*
552×associate-*l*
414×*-commutative
383×exp-prod
238×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
094732340
1204230405
2722230284
Stop Event
1×node limit
Counts
734 → 575
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))))
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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) 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)))))
(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 (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)))))
(*.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)))))
(*.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)))))
(*.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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(*.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)))))
(*.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)))))
(*.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)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.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)
(/.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)
(/.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)
(*.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)))))
(*.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)) (*.f64 (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))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (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))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
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(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)))))))
#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))))))))
(+.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))))))))
(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)))))))
(*.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 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.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 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.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 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.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 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.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 (+.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 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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)))))))))
(*.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 (+.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 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (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)))))))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.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 (*.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) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.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 (*.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) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.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 (*.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) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.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 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.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)
(/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/4 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 -1/2 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)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.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)
(*.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)))))))))
(*.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)))))))))
(*.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)))))))))
(*.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)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (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)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (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)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (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)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (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)))))))))
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))
(*.f64 #s(literal -1 binary64) k)
(*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))
(*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))
(*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) k)
(*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))
(*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))
(*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) 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 (*.f64 n (PI.f64)) 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)))
(*.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)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #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 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (+.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 (sqrt.f64 n) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 n) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))))
(*.f64 (pow.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.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 (sqrt.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 (cbrt.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)))) (pow.f64 (cbrt.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 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (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 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))
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(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 k) (neg.f64 k))) (-.f64 #s(literal 1 binary64) (neg.f64 k)))
(pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(log.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (-.f64 #s(literal 1 binary64) k))))
(cbrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (-.f64 #s(literal 1 binary64) k)))
(log1p.f64 (expm1.f64 (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (log1p.f64 (neg.f64 k)))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (cbrt.f64 #s(literal 2 binary64)) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(log.f64 (exp.f64 (sqrt.f64 #s(literal 2 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 #s(literal 2 binary64)))))
(cbrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 #s(literal 2 binary64))))
(log1p.f64 (expm1.f64 (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 1 binary64))
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (neg.f64 (*.f64 n (PI.f64))) (neg.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))
(sqrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) k)) n))
(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 n #s(literal 3 binary64)) (pow.f64 (/.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 (*.f64 n (PI.f64)) #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)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #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))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #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)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(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)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(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)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(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)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(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)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(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)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(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)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(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)))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(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 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(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 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(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 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(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 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(*.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 n (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k (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))))
(fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))))) (*.f64 k #s(literal 1/8 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))))
(fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64)) (*.f64 k (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal -1/48 binary64)))) (pow.f64 k #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))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
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(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) k) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64))
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(+.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))))))))
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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)))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
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(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)
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(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
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(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
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(pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) #s(literal 2 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(exp.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))

eval115.0ms (0.8%)

Compiler

Compiled 18108 to 2858 computations (84.2% saved)

prune127.0ms (0.9%)

Pruning

19 alts after pruning (15 fresh and 4 done)

PrunedKeptTotal
New87111882
Fresh13417
Picked235
Done011
Total88619905
Accuracy
100.0%
Counts
905 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.8%
(/.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))
▶98.8%
(/.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))))))
✓98.8%
(*.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)))
69.6%
(*.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)))) (pow.f64 k #s(literal -1/2 binary64))))
46.8%
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
35.8%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓98.5%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
46.5%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)))
46.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
▶35.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
35.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
35.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
✓35.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
▶88.3%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
88.4%
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
▶88.5%
(sqrt.f64 (*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
36.0%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
▶36.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
24.3%
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 3 binary64)))
Compiler

Compiled 488 to 367 computations (24.8% saved)

localize430.0ms (3%)

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-diff128
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
✓cost-diff128
(sqrt.f64 (*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
cost-diff0
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓cost-diff0
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))
✓cost-diff0
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
✓cost-diff0
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
✓cost-diff0
(/.f64 n (/.f64 k (PI.f64)))
✓cost-diff0
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
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)
accuracy99.8%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy99.2%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
✓accuracy88.6%
(sqrt.f64 (*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
accuracy49.3%
(PI.f64)
accuracy99.8%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy99.7%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))
✓accuracy88.6%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
accuracy49.3%
(PI.f64)
✓accuracy99.8%
(/.f64 n (/.f64 k (PI.f64)))
✓accuracy99.6%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
✓accuracy88.6%
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
accuracy49.3%
(PI.f64)
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
✓accuracy99.8%
(*.f64 (PI.f64) (/.f64 n k))
✓accuracy88.6%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
accuracy49.3%
(PI.f64)
accuracy99.8%
(*.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)))))
✓accuracy98.9%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
accuracy49.3%
(PI.f64)
Rules
191×associate-*r*
137×associate-*l*
97×times-frac
94×associate-*r/
59×associate-*l/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040865
174865
2151831
3327831
4698831
5887831
6934831
71018831
81099831
91104831
101105831
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 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 n (/.f64 k (PI.f64)))
n
(/.f64 k (PI.f64))
k
(PI.f64)
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.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 binary64) k)
#s(literal 1 binary64)
k
(sqrt.f64 (*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.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)
(/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) 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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -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))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.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 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 #s(literal 2 binary64) (/.f64 n k))))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k)))
(*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))
#s(literal 2 binary64)
(*.f64 (PI.f64) (/.f64 n k))
(PI.f64)
(/.f64 n k)
n
k
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
n
(/.f64 k (PI.f64))
k
(PI.f64)
(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 #s(literal 2 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.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 binary64) k)
#s(literal 1 binary64)
k
(sqrt.f64 (*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (*.f64 n (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 n (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)))
(*.f64 n (/.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 n (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k))
(/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) k)
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
Results
159.0ms122×0valid
108.0ms59×5exit
35.0ms75×0unsamplable
Compiler

Compiled 241 to 35 computations (85.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 209.0ms
ival-sqrt: 123.0ms (58.7% of total)
ival-pow: 31.0ms (14.8% of total)
ival-mult: 18.0ms (8.6% of total)
backward-pass: 17.0ms (8.1% of total)
ival-div: 15.0ms (7.2% of total)
ival-sub: 3.0ms (1.4% of total)
const: 1.0ms (0.5% of total)
ival-pi: 1.0ms (0.5% of total)

series160.0ms (1.1%)

Counts
15 → 348
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 n (/.f64 k (PI.f64))))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))>
#<alt (/.f64 n (/.f64 k (PI.f64)))>
#<alt (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))>
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))>
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
#<alt (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)>
#<alt (*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) 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))))>
#<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 (*.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 (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 (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 (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 (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 (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 (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 (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 (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 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.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)))))>
#<alt (+.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)))))>
#<alt (+.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)))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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)))))))>
#<alt (*.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)))))))>
#<alt (*.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)))))))>
#<alt (*.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)))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<alt (*.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))))))>
#<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)))>
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#<alt (/.f64 (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 binary64) k))) k)>
#<alt (/.f64 (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 binary64) k))) k)>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k (+.f64 (*.f64 #s(literal -2 binary64) (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))) k)>
#<alt (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k (+.f64 (*.f64 #s(literal -2 binary64) (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)))))) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) k)>
#<alt (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k)>
#<alt (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k)>
#<alt (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k)>
#<alt (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k)>
#<alt (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)>
#<alt (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)>
#<alt (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)>
#<alt (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k (+.f64 (*.f64 #s(literal -2 binary64) (*.f64 k (+.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 -2 binary64) (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))) k)>
#<alt (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k (+.f64 (*.f64 #s(literal -2 binary64) (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 k (+.f64 (*.f64 #s(literal -2 binary64) (*.f64 k (+.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 #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 -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)))))))))))) k)>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
Calls

87 calls:

TimeVariablePointExpression
58.0ms
k
@-inf
(/ (sqrt k) (pow (* 2 (* (PI) n)) (- 1/2 (* k 1/2))))
34.0ms
n
@inf
(* (* n (* 2 (PI))) (/ (/ 1 k) (pow (* n (* 2 (PI))) k)))
5.0ms
n
@-inf
(* (* n (* 2 (PI))) (/ (/ 1 k) (pow (* n (* 2 (PI))) k)))
4.0ms
k
@-inf
(sqrt (/ (pow (* n (* 2 (PI))) (- 1 k)) k))
3.0ms
k
@0
(sqrt (* (* n (* 2 (PI))) (/ (/ 1 k) (pow (* n (* 2 (PI))) k))))

rewrite158.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
292×log1p-expm1-u
292×expm1-log1p-u
286×add-exp-log
286×pow1
285×add-log-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
039547
1723527
Stop Event
1×node limit
Counts
15 → 439
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 n (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(/.f64 n (/.f64 k (PI.f64)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (neg.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 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 (sqrt.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 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 (PI.f64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (sqrt.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(fabs.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (cbrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))))
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(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(*.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (neg.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 k)))
(*.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) k))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) k))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) 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 binary64) k)) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64))
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) 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 binary64) k)) 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 binary64) k)) k))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #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 binary64) k)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))) #s(literal 1 binary64))
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(/.f64 (neg.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 n) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)) #s(literal 3 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3/2 binary64)) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(exp.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))) #s(literal 1 binary64)))

simplify425.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
746×associate-*l*
375×fma-define
374×associate-*r/
343×associate-*l/
328×*-commutative
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0119838793
1282937476
Stop Event
1×node limit
Counts
787 → 725
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))))
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(+.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))))
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(fabs.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(*.f64 (pow.f64 n k) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (pow.f64 n k))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) k)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
(*.f64 (pow.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(*.f64 (pow.f64 #s(literal 2 binary64) k) (pow.f64 (*.f64 (PI.f64) n) k))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) k) (pow.f64 #s(literal 2 binary64) k))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64))) k) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) k) (pow.f64 (PI.f64) k))
(sqrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) k))
(log.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(exp.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #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))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (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))) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k))
(*.f64 (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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(*.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (neg.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 k)))
(*.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) k))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) k))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) 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 binary64) k)) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64))
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) 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 binary64) k)) 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 binary64) k)) k))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #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 binary64) k)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))) #s(literal 1 binary64))
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(/.f64 (neg.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 n) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)) #s(literal 3 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3/2 binary64)) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(exp.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))) #s(literal 1 binary64)))
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 #s(literal 1/2 binary64) k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #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 #s(literal 1/2 binary64) k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #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 #s(literal 1/2 binary64) k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #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))))
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#s(literal 1 binary64)
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(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))))))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n)))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3 binary64)))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) #s(literal 8 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)) #s(literal 3 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (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 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) #s(literal 8 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3/2 binary64)) (pow.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k))) #s(literal 3/2 binary64))))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n)))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n)))))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n)))
(exp.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) k)))) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n)))

eval165.0ms (1.1%)

Compiler

Compiled 20769 to 3726 computations (82.1% saved)

prune218.0ms (1.5%)

Pruning

31 alts after pruning (24 fresh and 7 done)

PrunedKeptTotal
New991191010
Fresh5510
Picked145
Done134
Total998311029
Accuracy
100.0%
Counts
1029 → 31
Alt Table
Click to see full alt table
StatusAccuracyProgram
22.8%
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
35.8%
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓98.8%
(/.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))
36.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
✓98.8%
(/.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))))))
▶98.8%
(/.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 #s(literal 1/2 binary64) k)))))
✓98.8%
(*.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)))
46.8%
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
35.8%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
35.9%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
46.5%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)))
▶35.8%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
47.1%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
▶36.6%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
46.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
✓35.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
✓35.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
✓88.3%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
▶74.8%
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
58.8%
(sqrt.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) (pow.f64 n k)) k))
36.0%
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
36.0%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
73.2%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n))))
36.0%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
▶36.0%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
36.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
✓36.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
36.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
33.7%
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
24.2%
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))) #s(literal 3/2 binary64)))
24.2%
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
Compiler

Compiled 721 to 569 computations (21.1% saved)

localize244.0ms (1.7%)

Algorithm
1×egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
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
(/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
✓cost-diff0
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
✓cost-diff0
(sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff128
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
cost-diff0
(/.f64 (PI.f64) k)
✓cost-diff0
(*.f64 n #s(literal 2 binary64))
✓cost-diff0
(*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k))
✓cost-diff0
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) 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
(sqrt.f64 k)
✓accuracy99.7%
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
accuracy99.2%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
✓accuracy88.6%
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
accuracy71.6%
(PI.f64)
✓accuracy99.7%
(/.f64 (/.f64 k (PI.f64)) n)
✓accuracy99.5%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
✓accuracy89.3%
(sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))
accuracy71.6%
(PI.f64)
✓accuracy99.4%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
✓accuracy98.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy88.5%
(sqrt.f64 (/.f64 n k))
accuracy71.6%
(PI.f64)
✓accuracy99.7%
(*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k))
accuracy99.7%
(/.f64 (PI.f64) k)
✓accuracy88.5%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
accuracy71.6%
(PI.f64)
accuracy99.8%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy99.7%
(*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
✓accuracy98.9%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
accuracy71.6%
(PI.f64)
Rules
33×associate-/l*
33×associate-*l*
32×*-commutative
31×associate-*r*
26×associate-*r/
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
039779
167757
2112757
3203757
4278757
5282757
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.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 #s(literal 1/2 binary64) k)))))
#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 #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) (*.f64 #s(literal 1/2 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 1/2 binary64) k))
#s(literal -1/2 binary64)
(*.f64 #s(literal 1/2 binary64) k)
#s(literal 1/2 binary64)
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(/.f64 (PI.f64) k)
(PI.f64)
k
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
n
k
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))
(/.f64 (/.f64 k (PI.f64)) n)
(/.f64 k (PI.f64))
k
(PI.f64)
n
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.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
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
Outputs
(/.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 #s(literal 1/2 binary64) 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 #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)))))
#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 #s(literal 1/2 binary64) k))))
(*.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 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))))
(sqrt.f64 k)
k
(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))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #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 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 1/2 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))
#s(literal 1/2 binary64)
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
(*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(/.f64 (PI.f64) k)
(PI.f64)
k
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(sqrt.f64 (/.f64 n k))
(/.f64 n k)
n
k
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(/.f64 (/.f64 k (PI.f64)) n)
(/.f64 k (*.f64 n (PI.f64)))
(/.f64 k (PI.f64))
k
(PI.f64)
n
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(sqrt.f64 (/.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(sqrt.f64 (*.f64 n (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(/.f64 (*.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(*.f64 n (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (pow.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 (*.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
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
Results
76.0ms181×0valid
30.0ms75×0unsamplable
Compiler

Compiled 218 to 34 computations (84.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 62.0ms
ival-pow: 19.0ms (30.6% of total)
ival-mult: 14.0ms (22.5% of total)
ival-div: 12.0ms (19.3% of total)
ival-sqrt: 12.0ms (19.3% of total)
ival-add: 2.0ms (3.2% of total)
ival-pi: 1.0ms (1.6% of total)
const: 1.0ms (1.6% of total)
backward-pass: 0.0ms (0% of total)

series46.0ms (0.3%)

Counts
15 → 308
Calls
Call 1
Inputs
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))>
#<alt (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))>
#<alt (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k))>
#<alt (sqrt.f64 (/.f64 n k))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))>
#<alt (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))>
#<alt (/.f64 (/.f64 k (PI.f64)) n)>
#<alt (sqrt.f64 (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))>
#<alt (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)>
#<alt (*.f64 n #s(literal 2 binary64))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))>
#<alt (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))>
Outputs
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 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 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))))>
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#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))>
#<alt (exp.f64 (*.f64 #s(literal -1 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)))))>
#<alt (exp.f64 (*.f64 #s(literal -1 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)))))>
#<alt (exp.f64 (*.f64 #s(literal -1 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)))))>
#<alt (exp.f64 (*.f64 #s(literal -1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (+.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 1/2 binary64))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))>
#<alt (+.f64 (*.f64 k (+.f64 (*.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 1/2 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 1/2 binary64))))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))>
#<alt (+.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 1/2 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 1/2 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 1/2 binary64))))))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))>
#<alt (*.f64 (sqrt.f64 k) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 k) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 k) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 k) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (*.f64 (exp.f64 (*.f64 #s(literal -1 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))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (*.f64 (exp.f64 (*.f64 #s(literal -1 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))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (*.f64 (exp.f64 (*.f64 #s(literal -1 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))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 k) (*.f64 (exp.f64 (*.f64 #s(literal -1 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))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))>
#<alt (*.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 k) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
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#<alt (*.f64 (sqrt.f64 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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))))>
#<alt (*.f64 (sqrt.f64 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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 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)))>
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#<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))))>
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#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
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#<alt (*.f64 #s(literal 2 binary64) n)>
#<alt (*.f64 #s(literal 2 binary64) n)>
#<alt (*.f64 #s(literal 2 binary64) n)>
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#<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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
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#<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) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
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#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
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#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.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)))))))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k (+.f64 (*.f64 #s(literal -2 binary64) (*.f64 k (+.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 -2 binary64) (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))) k)>
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#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))>
Calls

81 calls:

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

rewrite150.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
285×associate-*r*
274×log1p-expm1-u
274×expm1-log1p-u
271×add-exp-log
270×add-log-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
038481
1653463
Stop Event
1×node limit
Counts
15 → 458
Calls
Call 1
Inputs
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 (sqrt.f64 k) (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 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k))
(sqrt.f64 (/.f64 n k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 (/.f64 k (PI.f64)) n)
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)
(*.f64 n #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
Outputs
(-.f64 (exp.f64 (log1p.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))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 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))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
(*.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))) (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
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(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
(*.f64 (/.f64 n (pow.f64 n k)) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 n (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 n (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 n k)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (/.f64 #s(literal 1 binary64) k) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 n k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (/.f64 (PI.f64) k) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (/.f64 (PI.f64) k) #s(literal 1 binary64)) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 n k)) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (/.f64 (PI.f64) k) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 n k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 n k)) (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (pow.f64 n k)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (cbrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (cbrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (*.f64 n #s(literal 2 binary64)))) #s(literal -1 binary64))
(neg.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(neg.f64 (/.f64 (*.f64 n (neg.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)))
(log.f64 (exp.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(exp.f64 (log.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64)))

simplify567.0ms (3.9%)

Algorithm
1×egg-herbie
Rules
970×fma-define
388×associate-/l*
385×associate-*r/
311×*-commutative
310×associate-*l/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0110033402
1255132253
2702232073
Stop Event
1×node limit
Counts
766 → 666
Calls
Call 1
Inputs
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #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 (*.f64 #s(literal 1/2 binary64) k) #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 (*.f64 #s(literal 1/2 binary64) k) #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 (*.f64 #s(literal 1/2 binary64) k) #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 (*.f64 #s(literal 1/2 binary64) k) #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 (*.f64 #s(literal 1/2 binary64) k) #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 (*.f64 #s(literal 1/2 binary64) k) #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 (*.f64 #s(literal 1/2 binary64) k) #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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(*.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))))
(+.f64 (*.f64 k (+.f64 (*.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 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 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 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))) (*.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 1/2 binary64))))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 #s(literal -1 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)))))
(exp.f64 (*.f64 #s(literal -1 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)))))
(exp.f64 (*.f64 #s(literal -1 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)))))
(exp.f64 (*.f64 #s(literal -1 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 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
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(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)))
(*.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (/.f64 n k))
(*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (/.f64 (PI.f64) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
(*.f64 (/.f64 n (pow.f64 n k)) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 n (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 n (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 n k)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (/.f64 #s(literal 1 binary64) k) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 n k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (/.f64 (PI.f64) k) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (/.f64 (PI.f64) k) #s(literal 1 binary64)) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 n k)) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (/.f64 (PI.f64) k) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 n k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 n k)) (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (pow.f64 n k)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (cbrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (cbrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (*.f64 n #s(literal 2 binary64)))) #s(literal -1 binary64))
(neg.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(neg.f64 (/.f64 (*.f64 n (neg.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)))
(log.f64 (exp.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(exp.f64 (log.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64)))
Outputs
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal 1/2 binary64) k #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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal 1/2 binary64) k #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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal 1/2 binary64) k #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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal 1/2 binary64) k #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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal 1/2 binary64) k #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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(pow.f64 (exp.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))))
(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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(pow.f64 (exp.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))))
(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 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
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(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(/.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k))
(*.f64 (/.f64 (PI.f64) k) (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 2 binary64))) (/.f64 (cbrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal 2 binary64))) (/.f64 (cbrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (pow.f64 n k)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 2 binary64))) (pow.f64 n k)) (/.f64 (cbrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)))
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal 2 binary64))) (/.f64 (cbrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) (pow.f64 n k))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))) (cbrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 (cbrt.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal 2 binary64) k)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal 2 binary64))) (/.f64 (cbrt.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) k)))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)) (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)) (/.f64 (cbrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) k)))
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(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (cbrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (cbrt.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))) (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))) (cbrt.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))))
(pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 3 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(pow.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))) #s(literal 2 binary64)))
(fabs.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(pow.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (*.f64 n #s(literal 2 binary64)))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 k (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (*.f64 n #s(literal 2 binary64)))
(neg.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(neg.f64 (/.f64 (*.f64 n (neg.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))) #s(literal 2 binary64)))
(fabs.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(log.f64 (exp.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 3 binary64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(exp.f64 (log.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 n k) (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))

eval199.0ms (1.4%)

Compiler

Compiled 19427 to 3621 computations (81.4% saved)

prune230.0ms (1.6%)

Pruning

34 alts after pruning (26 fresh and 8 done)

PrunedKeptTotal
New1011161027
Fresh91019
Picked235
Done257
Total1024341058
Accuracy
100.0%
Counts
1058 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
22.5%
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
35.4%
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
22.8%
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
✓98.8%
(/.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))
46.6%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
36.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
36.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
36.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
✓98.8%
(*.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)))
35.8%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
46.9%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
35.9%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
46.5%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
✓35.8%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
46.5%
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
36.6%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1/2 binary64)))
✓36.6%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
✓35.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
✓88.3%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
✓74.8%
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
58.8%
(sqrt.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) (pow.f64 n k)) k))
36.0%
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
36.0%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
36.0%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
36.0%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
34.7%
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k) #s(literal 1 binary64))))
17.0%
(sqrt.f64 (*.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 (PI.f64) k)))
35.6%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
✓36.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
88.5%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
36.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
33.4%
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
24.2%
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))) #s(literal 3/2 binary64)))
23.8%
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
Compiler

Compiled 1353 to 594 computations (56.1% saved)

regimes92.0ms (0.6%)

Counts
70 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(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))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 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))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.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 n (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 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 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 (PI.f64) k)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(*.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) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (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)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 k n))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.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 #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 #s(literal 1/2 binary64) k)))))
(/.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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 3 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
(*.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 (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 1/4 binary64)) #s(literal 2 binary64)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (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))
(sqrt.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k))) (pow.f64 n k)) k))
(*.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)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 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 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 (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) k))))
(*.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)) (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 (*.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)))) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) 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)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (*.f64 k (*.f64 k (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))))
Outputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
Calls

4 calls:

32.0ms
(*.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
98.8%1k
98.8%1n
98.8%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))))
98.8%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes27.0ms (0.2%)

Counts
39 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(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))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 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))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.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 n (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 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 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 (PI.f64) k)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(*.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) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #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 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)))
Outputs
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
Calls

2 calls:

13.0ms
k
11.0ms
n
Results
AccuracySegmentsBranch
99.2%2k
90.1%2n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes64.0ms (0.4%)

Counts
37 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(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))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 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))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.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 n (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 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 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 (PI.f64) k)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(*.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) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #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 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k) #s(literal 1 binary64))))
Calls

2 calls:

51.0ms
k
10.0ms
n
Results
AccuracySegmentsBranch
50.1%3n
54.7%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts
27 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(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))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 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))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.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 n (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 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 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 (PI.f64) k)))
Outputs
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
Calls

2 calls:

9.0ms
k
8.0ms
n
Results
AccuracySegmentsBranch
46.9%1n
46.9%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes12.0ms (0.1%)

Counts
16 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(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))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 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))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.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 n (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
Calls

2 calls:

6.0ms
n
5.0ms
k
Results
AccuracySegmentsBranch
46.5%1k
46.5%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

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

2 calls:

4.0ms
n
4.0ms
k
Results
AccuracySegmentsBranch
36.7%1k
36.7%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0%)

Accuracy

Total -0.3b remaining (-0.8%)

Threshold costs -0.3b (-0.8%)

Counts
8 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(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))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
Calls

2 calls:

3.0ms
n
3.0ms
k
Results
AccuracySegmentsBranch
36.0%1k
36.0%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch21.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
19.0ms
2.05471579314241e-23
9.963117033262396e-21
Results
15.0ms128×0valid
Compiler

Compiled 239 to 193 computations (19.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 3.0ms (27.3% of total)
ival-pow: 3.0ms (27.3% of total)
ival-div: 2.0ms (18.2% of total)
ival-sub: 1.0ms (9.1% of total)
ival-sqrt: 1.0ms (9.1% 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
1.3039329358206162e+63
2.60040470026536e+64
Results
15.0ms112×0valid
Compiler

Compiled 205 to 171 computations (16.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-pow: 4.0ms (35.3% of total)
ival-div: 3.0ms (26.5% of total)
ival-mult: 2.0ms (17.7% of total)
ival-sub: 1.0ms (8.8% of total)
ival-sqrt: 1.0ms (8.8% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
055369
175369
284369
390369
494369
595369
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.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 7443676776395529/5316911983139663491615228241121378304 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 3300000000000000172662497344362713952852089265324095700270579712 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.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))
(if (<=.f64 k #s(literal 7443676776395529/5316911983139663491615228241121378304 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 7443676776395529/5316911983139663491615228241121378304 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 3300000000000000172662497344362713952852089265324095700270579712 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
(if (<=.f64 k #s(literal 3300000000000000172662497344362713952852089265324095700270579712 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))

soundness2.1s (14.4%)

Rules
1096×log1p-expm1-u
970×fma-define
724×fma-define
717×associate-*r*
552×associate-*l*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026274
1427270
24798270
059819230
1121217176
2421516542
039438
196380
2211380
3410364
4686352
51171352
61433352
71698352
82017352
92060352
102088352
112099352
122101352
0110033402
1255132253
2702232073
038481
1653463
094732340
1204230405
2722230284
042479
1706453
Stop Event
1×fuel
1×node limit
1×node limit
1×node limit
1×node limit
1×saturated
1×node limit
1×node limit
Compiler

Compiled 1126 to 376 computations (66.6% saved)

preprocess46.0ms (0.3%)

Compiler

Compiled 238 to 116 computations (51.3% saved)

end0.0ms (0%)

Profiling

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