Migdal et al, Equation (51)

Time bar (total: 49.6s)

analyze512.0ms (1%)

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

Compiled 19 to 14 computations (26.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 278.0ms
ival-pow: 112.0ms (40.3% of total)
ival-mult: 63.0ms (22.6% of total)
ival-sqrt: 35.0ms (12.6% of total)
ival-div: 25.0ms (9% of total)
ival-sub: 16.0ms (5.8% of total)
const: 15.0ms (5.4% of total)
ival-pi: 11.0ms (4% of total)
backward-pass: 1.0ms (0.4% of total)

sample14.5s (29.2%)

Results
3.5s8256×0valid
5.4s3860×5exit
1.7s1950×1invalid
117.0ms440×0invalid
118.0ms226×0unsamplable
Precisions
Click to see histograms. Total time spent on operations: 8.0s
ival-pow: 2.9s (35.7% of total)
ival-mult: 1.8s (22.2% of total)
ival-div: 1.0s (12.8% of total)
backward-pass: 710.0ms (8.8% of total)
ival-sqrt: 616.0ms (7.7% of total)
ival-pi: 521.0ms (6.5% of total)
ival-sub: 413.0ms (5.1% of total)
const: 90.0ms (1.1% of total)
Bogosity

preprocess401.0ms (0.8%)

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))

explain484.0ms (1%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2220(2.3919219994066362e-253 5.917908853259395e-185)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
288.0ms512×0valid
Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 152.0ms
ival-pow: 43.0ms (28.3% of total)
ival-sqrt: 37.0ms (24.4% of total)
ival-div: 28.0ms (18.5% of total)
ival-sub: 21.0ms (13.8% of total)
ival-mult: 17.0ms (11.2% of total)
ival-pi: 3.0ms (2% of total)
const: 2.0ms (1.3% of total)
backward-pass: 0.0ms (0% of total)

eval1.0ms (0%)

Compiler

Compiled 59 to 23 computations (61% saved)

prune3.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 34 to 25 computations (26.5% saved)

localize1.0s (2%)

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)
✓accuracy99.8%
(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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.8%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓accuracy99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
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
887.0ms256×0valid
Compiler

Compiled 105 to 21 computations (80% saved)

Precisions
Click to see histograms. Total time spent on operations: 388.0ms
ival-div: 245.0ms (63.1% of total)
ival-pow: 56.0ms (14.4% of total)
ival-sub: 43.0ms (11.1% of total)
ival-mult: 38.0ms (9.8% of total)
ival-sqrt: 4.0ms (1% of total)
ival-pi: 2.0ms (0.5% of total)
const: 1.0ms (0.3% of total)
backward-pass: 0.0ms (0% of total)

series504.0ms (1%)

Counts
12 → 160
Calls
Call 1
Inputs
#<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 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) 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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))>
#<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 (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 #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))))>
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#<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))))>
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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 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 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<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 (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)))))>
#<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)))))>
#<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 (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 #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
220.0ms
n
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
119.0ms
n
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
30.0ms
n
@inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
21.0ms
k
@inf
(/ 1 (sqrt k))
15.0ms
k
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite1.2s (2.4%)

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
(/.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 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) 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))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(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 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (cbrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (/.f64 #s(literal 1 binary64) k)) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(log.f64 (exp.f64 (pow.f64 k #s(literal -1/2 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 k #s(literal -1/2 binary64)))))
(cbrt.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64))))
(log1p.f64 (expm1.f64 (pow.f64 k #s(literal -1/2 binary64))))
(exp.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))) #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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 n) (*.f64 #s(literal 2 binary64) (PI.f64))))
(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))))
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(*.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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 n) (*.f64 #s(literal 2 binary64) (PI.f64))))
(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))) (pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 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)))

simplify1.2s (2.5%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
059819152
1121017098
2421016476
Stop Event
1×node limit
Counts
459 → 405
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.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 (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)) (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 (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 (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 (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)))))
(*.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 #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 #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)))))
(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)))
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(exp.f64 (log.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))))))
(exp.f64 (*.f64 (log.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 (exp.f64 (log1p.f64 (PI.f64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.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 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 n) (*.f64 #s(literal 2 binary64) (PI.f64))))
(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))) (pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 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
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (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 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) #s(literal -1/2 binary64)))) k)
(/.f64 (fma.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) 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 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))) #s(literal 1/8 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) k)
(/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (*.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))) #s(literal 1/8 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) k))))) 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 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) #s(literal 2 binary64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k)
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(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(log.f64 (pow.f64 (exp.f64 n) (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.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 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.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 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(expm1.f64 (log1p.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
(+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 k #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (*.f64 k #s(literal 1/2 binary64))))
(+.f64 #s(literal -1 binary64) (fma.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 k #s(literal -1/2 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 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 k) #s(literal 2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(*.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(*.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 k #s(literal 1/2 binary64))
(*.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 k #s(literal 1/2 binary64))
(*.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 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(*.f64 (neg.f64 k) #s(literal -1/2 binary64))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(pow.f64 (cbrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 3 binary64))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 2 binary64))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1 binary64))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(neg.f64 (*.f64 k #s(literal -1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(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))))
(sqrt.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(fabs.f64 (*.f64 k #s(literal -1/2 binary64)))
(log.f64 (sqrt.f64 (exp.f64 k)))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(cbrt.f64 (pow.f64 (*.f64 k #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(expm1.f64 (log1p.f64 (*.f64 k #s(literal 1/2 binary64))))
(+.f64 #s(literal -1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(exp.f64 (log.f64 (*.f64 k #s(literal 1/2 binary64))))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(exp.f64 (*.f64 (log.f64 (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 k #s(literal -1/2 binary64))

eval300.0ms (0.6%)

Compiler

Compiled 9520 to 1543 computations (83.8% saved)

prune353.0ms (0.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New44115456
Fresh000
Picked112
Done000
Total44216458
Accuracy
100.0%
Counts
458 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.9%
(pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (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))
68.0%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
✓99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶96.2%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
99.3%
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))))
95.9%
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
99.6%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
▶48.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
67.7%
(*.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)))))
38.6%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶99.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
38.6%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
▶38.6%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
▶38.3%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
89.9%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) k))
Compiler

Compiled 516 to 386 computations (25.2% saved)

localize1.2s (2.4%)

Algorithm
1×egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
✓cost-diff256
(/.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))))
✓cost-diff6528
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 k)
cost-diff64
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓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 (PI.f64) k)
✓cost-diff0
(*.f64 n (/.f64 (PI.f64) k))
✓cost-diff0
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
✓cost-diff0
(/.f64 #s(literal 1 binary64) k)
✓cost-diff64
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓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)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
accuracy99.6%
(PI.f64)
accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy92.4%
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
✓accuracy99.6%
(*.f64 n (PI.f64))
accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓accuracy99.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓accuracy99.3%
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)
accuracy99.6%
(PI.f64)
✓accuracy99.6%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
✓accuracy89.8%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
accuracy99.6%
(PI.f64)
✓accuracy99.6%
(/.f64 (PI.f64) k)
✓accuracy99.3%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy72.1%
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓accuracy99.7%
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓accuracy99.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy99.6%
(PI.f64)
accuracy99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Rules
49×fma-neg
39×*-commutative
29×associate-*r*
26×associate-*l*
24×times-frac
Iterations

Useful iterations: 7 (0.0ms)

IterNodesCost
045803
179797
2116797
3159797
4197773
5234757
6270757
7322753
8345753
9354753
10402753
11469753
12508753
13539753
14556753
15564753
16565753
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 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 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #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
(sqrt.f64 #s(literal 2 binary64))
#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))
(/.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
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
n
(PI.f64)
(sqrt.f64 #s(literal 2 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)))) (exp.f64 (*.f64 (log.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
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(*.f64 (log.f64 k) #s(literal 1/2 binary64))
(log.f64 k)
Outputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(pow.f64 k #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #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 -1/2 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 (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)))
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -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))
(-.f64 #s(literal 1 binary64) k)
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
n
(/.f64 (PI.f64) k)
(PI.f64)
k
(sqrt.f64 #s(literal 2 binary64))
#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))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.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))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)
(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.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)
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1 binary64) k))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) 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
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(pow.f64 k #s(literal -1/2 binary64))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
n
(PI.f64)
(sqrt.f64 #s(literal 2 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)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(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 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #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 -1/2 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 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.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)))
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -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 2 binary64))
(*.f64 k #s(literal 1/2 binary64))
k
(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
(sqrt.f64 k)
(*.f64 (log.f64 k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (log.f64 k))
(log.f64 k)
Results
473.0ms255×0valid
33.0ms1×0invalid
Compiler

Compiled 234 to 40 computations (82.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 342.0ms
ival-div: 92.0ms (26.9% of total)
ival-pow: 90.0ms (26.3% of total)
ival-mult: 52.0ms (15.2% of total)
ival-sqrt: 47.0ms (13.7% of total)
ival-exp: 30.0ms (8.8% of total)
const: 17.0ms (5% of total)
ival-sub: 5.0ms (1.5% of total)
ival-log: 5.0ms (1.5% of total)
ival-pi: 2.0ms (0.6% of total)
ival-add: 2.0ms (0.6% of total)
backward-pass: 0.0ms (0% of total)

series205.0ms (0.4%)

Counts
17 → 260
Calls
Call 1
Inputs
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (PI.f64) k)>
#<alt (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))>
#<alt (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))>
#<alt (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 n (PI.f64))>
#<alt (exp.f64 (*.f64 (log.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)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))>
#<alt (/.f64 #s(literal 1 binary64) k)>
#<alt (*.f64 n (/.f64 (PI.f64) k))>
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
Outputs
#<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)) (*.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))))>
#<alt (*.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))))>
#<alt (*.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))))>
#<alt (*.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))))>
#<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 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
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#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
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#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
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#<alt (sqrt.f64 k)>
#<alt (sqrt.f64 k)>
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#<alt (sqrt.f64 k)>
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#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
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#<alt (/.f64 (*.f64 n (PI.f64)) k)>
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#<alt (/.f64 (*.f64 n (PI.f64)) k)>
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#<alt (/.f64 (*.f64 n (PI.f64)) k)>
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#<alt (/.f64 (*.f64 n (PI.f64)) k)>
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#<alt (/.f64 (*.f64 n (PI.f64)) k)>
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#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))>
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#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))>
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#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (+.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))))>
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#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))>
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#<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

78 calls:

TimeVariablePointExpression
26.0ms
k
@-inf
(* n (/ (PI) k))
18.0ms
k
@inf
(sqrt (/ (pow (* n (* 2 (PI))) (+ 1 k)) k))
15.0ms
n
@-inf
(* (sqrt (* n (/ (PI) k))) (sqrt 2))
6.0ms
k
@inf
(/ (pow (* n (* 2 (PI))) (+ 1 k)) k)
3.0ms
k
@0
(sqrt (/ (pow (* n (* 2 (PI))) (+ 1 k)) k))

rewrite841.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
291×log1p-expm1-u
291×expm1-log1p-u
289×add-exp-log
287×add-log-exp
287×pow1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
045451
1830443
Stop Event
1×node limit
Counts
17 → 409
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (PI.f64) k)
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 n (PI.f64))
(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)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) k)
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
Outputs
(-.f64 (exp.f64 (log1p.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.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 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.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 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal -1 binary64)) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(pow.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))
(pow.f64 (cbrt.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 3 binary64))
(pow.f64 (pow.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 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.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 2 binary64))
(pow.f64 (/.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))
(neg.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)))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) k))
(log.f64 (exp.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))))
(log.f64 (+.f64 #s(literal 1 binary64) (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)))))
(cbrt.f64 (pow.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 3 binary64)))
(cbrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3/2 binary64))) (pow.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 3 binary64))))
(cbrt.f64 (*.f64 (pow.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 3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3/2 binary64)))))
(cbrt.f64 (/.f64 (pow.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 3 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(expm1.f64 (log1p.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))))
(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 (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 k #s(literal -2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 k #s(literal -2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 k)))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3/2 binary64))) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(fabs.f64 (pow.f64 k #s(literal -1/2 binary64)))
(log.f64 (exp.f64 (pow.f64 k #s(literal -1/2 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 k #s(literal -1/2 binary64)))))
(cbrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64))))
(log1p.f64 (expm1.f64 (pow.f64 k #s(literal -1/2 binary64))))
(exp.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 2 binary64)))) (sqrt.f64 (cbrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (PI.f64) k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (PI.f64) (sqrt.f64 k)))
(*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64)) (cbrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) (neg.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (PI.f64) (cbrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) k))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 k)))
(pow.f64 (/.f64 (PI.f64) k) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(pow.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64))
(neg.f64 (/.f64 (PI.f64) (neg.f64 k)))
(neg.f64 (/.f64 (neg.f64 (PI.f64)) k))
(sqrt.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
(log.f64 (exp.f64 (/.f64 (PI.f64) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (PI.f64) k))))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (PI.f64) k)))
(log1p.f64 (expm1.f64 (/.f64 (PI.f64) k)))
(exp.f64 (log.f64 (/.f64 (PI.f64) k)))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k))))
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(log.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (PI.f64)) 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)))

simplify1.5s (3.1%)

Algorithm
1×egg-herbie
Rules
513×associate-*r*
487×associate-*l*
486×exp-prod
380×times-frac
360×*-commutative
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
095226802
1198125714
2702925228
Stop Event
1×node limit
Counts
669 → 629
Calls
Call 1
Inputs
(*.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))))
(*.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))))
(*.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)))))
(*.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 #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 #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)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.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)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))) k))
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(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 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))))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (/.f64 (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 (*.f64 n (PI.f64)) k)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (/.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 k (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.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))))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))) k)
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) k))) k))
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(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (*.f64 (PI.f64) n) k))))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(exp.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (PI.f64) n) k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 n (+.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 n (+.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))) (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1 binary64) k)) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (PI.f64) (+.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))))
(log.f64 (exp.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(exp.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 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))
(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 #s(literal 2 binary64)) (PI.f64)) 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)))
Outputs
(*.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 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(/.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 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.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 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 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 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 2 binary64)))) (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)))) 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 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (fma.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 3 binary64))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) #s(literal 1/8 binary64)) (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)))) 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)) (pow.f64 (exp.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)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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)) (pow.f64 (exp.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)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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)) (pow.f64 (exp.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)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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)) (pow.f64 (exp.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)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.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 (pow.f64 (exp.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 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 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 (pow.f64 (exp.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 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 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 (pow.f64 (exp.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 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 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 (pow.f64 (exp.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 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64)))
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(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 2 binary64) (*.f64 k #s(literal 2 binary64)))))
(log.f64 (exp.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 k #s(literal 1 binary64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal 1 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 k #s(literal 1 binary64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal 1 binary64)))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 k #s(literal 1 binary64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal 1 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 k #s(literal 1 binary64)))))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal 1 binary64)))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 k #s(literal 1 binary64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal 1 binary64)))
(exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 k #s(literal 1 binary64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 k #s(literal 1 binary64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 3 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) #s(literal 4 binary64)))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (PI.f64)) n))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))

eval501.0ms (1%)

Compiler

Compiled 15162 to 2807 computations (81.5% saved)

prune497.0ms (1%)

Pruning

20 alts after pruning (15 fresh and 5 done)

PrunedKeptTotal
New84210852
Fresh5510
Picked145
Done011
Total84820868
Accuracy
100.0%
Counts
868 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
68.0%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
✓99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓96.2%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
99.3%
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))))
48.1%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
95.9%
(/.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))
▶48.1%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
38.9%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal 1 binary64))))))
▶99.6%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
48.1%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
48.0%
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
▶38.5%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
✓99.6%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
38.6%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓38.6%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
89.9%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
✓38.3%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
38.7%
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
▶38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
▶36.2%
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
Compiler

Compiled 494 to 385 computations (22.1% saved)

localize940.0ms (1.9%)

Algorithm
1×egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
✓cost-diff0
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
✓cost-diff0
(log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
✓cost-diff12800
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
cost-diff0
(sqrt.f64 k)
✓cost-diff0
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
✓cost-diff0
(/.f64 k (PI.f64))
✓cost-diff0
(/.f64 n (/.f64 k (PI.f64)))
✓cost-diff0
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(/.f64 (*.f64 (PI.f64) n) k)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
✓cost-diff0
(*.f64 k #s(literal 1/2 binary64))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 (PI.f64) n)
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
accuracy99.6%
(PI.f64)
accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy91.9%
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
✓accuracy72.1%
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
accuracy99.6%
(PI.f64)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy99.4%
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
accuracy99.6%
(PI.f64)
✓accuracy99.6%
(/.f64 k (PI.f64))
✓accuracy99.3%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy72.1%
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
✓accuracy99.7%
(/.f64 (*.f64 (PI.f64) n) k)
accuracy99.6%
(PI.f64)
accuracy99.6%
(*.f64 (PI.f64) n)
✓accuracy72.1%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
✓accuracy99.8%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
✓accuracy99.7%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
accuracy99.6%
(PI.f64)
accuracy99.6%
(*.f64 (PI.f64) n)
Rules
24×*-commutative
24×fma-define
16×sub-neg
12×associate-*r*
12×associate-*l*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036701
159701
290683
3136683
4179683
5207683
6239683
7268683
8279683
9280683
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 1/2 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 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))
k
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
#s(literal 2 binary64)
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #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 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 k)
k
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
Outputs
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (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 1/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
k
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))
#s(literal 2 binary64)
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) n)
(PI.f64)
n
k
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
n
(/.f64 k (PI.f64))
k
(PI.f64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 k)
k
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))))
(log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
Results
647.0ms255×0valid
1.0ms1×0invalid
Compiler

Compiled 197 to 31 computations (84.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 467.0ms
ival-exp: 224.0ms (48% of total)
ival-mult: 108.0ms (23.1% of total)
ival-sqrt: 43.0ms (9.2% of total)
ival-pow: 42.0ms (9% of total)
ival-div: 25.0ms (5.4% of total)
ival-log: 18.0ms (3.9% of total)
ival-sub: 3.0ms (0.6% of total)
ival-pi: 2.0ms (0.4% of total)
const: 2.0ms (0.4% of total)
backward-pass: 0.0ms (0% of total)

series997.0ms (2%)

Counts
18 → 372
Calls
Call 1
Inputs
#<alt (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))>
#<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 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))>
#<alt (/.f64 (*.f64 (PI.f64) n) k)>
#<alt (sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 k (PI.f64))>
#<alt (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))>
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))>
#<alt (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))>
#<alt (exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
#<alt (*.f64 k #s(literal 1/2 binary64))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))>
#<alt (/.f64 n (/.f64 k (PI.f64)))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))>
#<alt (log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))>
#<alt (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)>
Outputs
#<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)))))>
#<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)))))>
#<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)))))>
#<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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<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 (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)))))>
#<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)) (*.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)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<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 (*.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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 #s(literal 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)>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.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 (*.f64 n (PI.f64)) k)>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (*.f64 k n))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 k)))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 k)))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 k)))>
#<alt (+.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1 binary64) (log.f64 k)))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (log.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))>
Calls

96 calls:

TimeVariablePointExpression
376.0ms
n
@0
(/ (* (PI) n) k)
158.0ms
n
@0
(log (sqrt (/ (* 2 (* (PI) n)) k)))
85.0ms
n
@-inf
(log (sqrt (/ (* 2 (* (PI) n)) k)))
75.0ms
k
@-inf
(log (sqrt (/ (* 2 (* (PI) n)) k)))
73.0ms
k
@0
(log (sqrt (/ (* 2 (* (PI) n)) k)))

rewrite1.1s (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
239×pow1
239×log1p-expm1-u
239×expm1-log1p-u
235×add-exp-log
235×add-cube-cbrt
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036497
1588497
27645497
Stop Event
1×node limit
Counts
18 → 844
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 1/2 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 1/2 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(/.f64 (*.f64 (PI.f64) n) k)
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 k (PI.f64))
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 n (/.f64 k (PI.f64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)
Outputs
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.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))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) k)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(log.f64 (+.f64 #s(literal 1 binary64) (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)))) (pow.f64 k #s(literal -1/2 binary64))))))
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(*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (log.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))))))
(*.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))))
(*.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))))
(pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(neg.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))))))
(sqrt.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 2 binary64)))
(cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))))
(log1p.f64 (-.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))))
(exp.f64 (*.f64 (log.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))
(*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))
(*.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (sqrt.f64 k)))
(*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))
(*.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) (*.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64))) (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))
(*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (PI.f64) n) (sqrt.f64 k)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) (sqrt.f64 k)) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 2 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (*.f64 (PI.f64) n) (cbrt.f64 k)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))
(*.f64 (/.f64 (*.f64 (PI.f64) n) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (cbrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (cbrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (sqrt.f64 k)) (/.f64 n (sqrt.f64 k)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64)) (/.f64 n k))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 n (cbrt.f64 k)))
(*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) #s(literal -2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1 binary64))
(neg.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 k)))
(neg.f64 (/.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) k))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(exp.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1 binary64)))

simplify2.8s (5.6%)

Algorithm
1×egg-herbie
Rules
704×fma-define
465×exp-prod
416×cube-prod
361×associate-*r/
289×*-commutative
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0114847848
1245346452
2609945874
Stop Event
1×node limit
Counts
1216 → 873
Calls
Call 1
Inputs
(*.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)))))
(*.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)))))
(*.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)))))
(*.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)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 (*.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)
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(+.f64 (fma.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (neg.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))) (fma.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64) (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(+.f64 (fma.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (neg.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal 1 binary64)))) (fma.f64 (neg.f64 (log.f64 (sqrt.f64 k))) #s(literal 1 binary64) (*.f64 (log.f64 (sqrt.f64 k)) #s(literal 1 binary64))))
(+.f64 (fma.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (neg.f64 (*.f64 (cbrt.f64 (log.f64 (sqrt.f64 k))) (*.f64 (cbrt.f64 (log.f64 (sqrt.f64 k))) (cbrt.f64 (log.f64 (sqrt.f64 k))))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 (sqrt.f64 k)))) (*.f64 (cbrt.f64 (log.f64 (sqrt.f64 k))) (cbrt.f64 (log.f64 (sqrt.f64 k)))) (*.f64 (cbrt.f64 (log.f64 (sqrt.f64 k))) (*.f64 (cbrt.f64 (log.f64 (sqrt.f64 k))) (cbrt.f64 (log.f64 (sqrt.f64 k)))))))
(+.f64 (fma.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))) (neg.f64 (log.f64 (sqrt.f64 k)))) (fma.f64 (neg.f64 (sqrt.f64 (log.f64 (sqrt.f64 k)))) (sqrt.f64 (log.f64 (sqrt.f64 k))) (log.f64 (sqrt.f64 k))))
(-.f64 #s(literal 0 binary64) (log.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))))))
(-.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (log.f64 (sqrt.f64 k)))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))) #s(literal 1 binary64))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64)))))))
(*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 #s(literal 1 binary64) (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (log.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))))))
(*.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))))
(*.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))))
(pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(neg.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))))))
(sqrt.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 2 binary64)))
(cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))))
(log1p.f64 (-.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))))
(exp.f64 (*.f64 (log.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))
(*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))
(*.f64 (*.f64 (PI.f64) n) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 1 binary64) k))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (sqrt.f64 k)))
(*.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))
(*.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 1 binary64) (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) (*.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64))) (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k))
(*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 k)) (/.f64 (*.f64 (PI.f64) n) (sqrt.f64 k)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) (sqrt.f64 k)) (/.f64 #s(literal 2 binary64) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 2 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (*.f64 (PI.f64) n) (cbrt.f64 k)))
(*.f64 (/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) k))
(*.f64 (/.f64 (*.f64 (PI.f64) n) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (cbrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (cbrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (sqrt.f64 k)) (/.f64 n (sqrt.f64 k)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64)) (/.f64 n k))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 n (cbrt.f64 k)))
(*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64)))) #s(literal -2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1 binary64))
(neg.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 k)))
(neg.f64 (/.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) k))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(exp.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1 binary64)))
Outputs
(*.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)))))
(*.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 k #s(literal -1/2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))
(*.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)))))
(*.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 k #s(literal -1/2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))
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(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 3 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(neg.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 k)))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(neg.f64 (/.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)) k))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 2 binary64)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 n) (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
(+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(exp.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))

eval580.0ms (1.2%)

Compiler

Compiled 18054 to 3765 computations (79.1% saved)

prune1.0s (2%)

Pruning

36 alts after pruning (31 fresh and 5 done)

PrunedKeptTotal
New1084261110
Fresh5510
Picked235
Done325
Total1094361130
Accuracy
100.0%
Counts
1130 → 36
Alt Table
Click to see full alt table
StatusAccuracyProgram
29.4%
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
▶39.4%
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
39.4%
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
✓99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓96.2%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
48.1%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
48.1%
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
48.1%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
71.6%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
▶95.9%
(/.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))
38.6%
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal -1/2 binary64)))
36.2%
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
▶39.4%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
✓48.1%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
38.6%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))))
48.1%
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
39.4%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))))
48.1%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓38.5%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
48.1%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
▶38.6%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
89.9%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
38.7%
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
38.7%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
38.7%
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
38.7%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
38.7%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
✓38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
36.5%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
▶38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
37.0%
(sqrt.f64 (expm1.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
36.2%
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
31.3%
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
Compiler

Compiled 847 to 688 computations (18.8% saved)

localize1.4s (2.9%)

Algorithm
1×egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 k (*.f64 n (PI.f64)))
✓cost-diff0
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
✓cost-diff0
(/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (/.f64 n k))
✓cost-diff0
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
✓cost-diff0
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 n (PI.f64))
cost-diff0
(*.f64 k #s(literal 1/2 binary64))
✓cost-diff0
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))
✓cost-diff0
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
✓cost-diff0
(/.f64 n k)
✓cost-diff0
(*.f64 (/.f64 n k) (PI.f64))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))
✓cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
✓cost-diff0
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
✓cost-diff192
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
✓cost-diff192
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
accuracy99.6%
(*.f64 n (PI.f64))
✓accuracy99.3%
(/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy71.6%
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
✓accuracy99.6%
(*.f64 (PI.f64) (/.f64 n k))
accuracy99.6%
(PI.f64)
✓accuracy99.3%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy72.1%
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
✓accuracy99.7%
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))
accuracy99.6%
(PI.f64)
accuracy99.6%
(*.f64 n (PI.f64))
✓accuracy71.5%
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))
✓accuracy99.6%
(*.f64 (/.f64 n k) (PI.f64))
accuracy99.6%
(PI.f64)
✓accuracy72.1%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
✓accuracy99.7%
(/.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))
accuracy99.6%
(PI.f64)
accuracy99.6%
(*.f64 n (PI.f64))
✓accuracy96.3%
(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))))
Rules
1033×fma-define
811×fma-neg
545×times-frac
434×div-sub
406×associate-/r*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037695
174695
2128673
3212673
4365673
5520673
6711673
71111673
81996673
92809673
103464673
114146673
125197673
136818673
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
n
(PI.f64)
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) k)
k
(sqrt.f64 k)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))
#s(literal 2 binary64)
(*.f64 (/.f64 n k) (PI.f64))
(/.f64 n k)
n
k
(PI.f64)
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))
(*.f64 k #s(literal 1/2 binary64))
k
#s(literal 1/2 binary64)
(*.f64 n (PI.f64))
n
(PI.f64)
#s(literal -1/2 binary64)
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(PI.f64)
(/.f64 n k)
n
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(/.f64 k (*.f64 n (PI.f64)))
k
(*.f64 n (PI.f64))
n
(PI.f64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
Outputs
(/.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 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 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 n (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 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 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)) (log.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
n
(PI.f64)
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(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)
k
(sqrt.f64 k)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (/.f64 n k) (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (PI.f64) (/.f64 (*.f64 #s(literal 2 binary64) n) k))
#s(literal 2 binary64)
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 n k)
n
k
(PI.f64)
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k n) (/.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 #s(literal 1/2 binary64) (PI.f64)))
(*.f64 #s(literal 1/2 binary64) (/.f64 k (*.f64 n (PI.f64))))
(*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
k
#s(literal 1/2 binary64)
(*.f64 n (PI.f64))
n
(PI.f64)
#s(literal -1/2 binary64)
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(PI.f64)
(/.f64 n k)
n
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(/.f64 k (*.f64 n (PI.f64)))
k
(*.f64 n (PI.f64))
n
(PI.f64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
Results
482.0ms255×0valid
0.0ms1×0invalid
Compiler

Compiled 197 to 32 computations (83.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 306.0ms
ival-div: 191.0ms (62.5% of total)
ival-mult: 54.0ms (17.7% of total)
ival-pow: 30.0ms (9.8% of total)
ival-sqrt: 15.0ms (4.9% of total)
ival-log: 6.0ms (2% of total)
ival-exp: 4.0ms (1.3% of total)
ival-pi: 2.0ms (0.7% of total)
ival-sub: 2.0ms (0.7% of total)
const: 1.0ms (0.3% of total)
backward-pass: 0.0ms (0% of total)

series387.0ms (0.8%)

Counts
17 → 304
Calls
Call 1
Inputs
#<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 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))>
#<alt (*.f64 (/.f64 n k) (PI.f64))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))>
#<alt (pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))>
#<alt (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))>
#<alt (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))>
#<alt (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (PI.f64) (/.f64 n k))>
#<alt (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))>
#<alt (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (/.f64 n k)>
#<alt (/.f64 k (*.f64 n (PI.f64)))>
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))))>
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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))))>
#<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)))>
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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))))>
#<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)))))>
#<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)))))>
#<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)))))>
#<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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 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)))))>
#<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)>
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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 -1/48 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 (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)))))>
#<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)))))>
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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 (*.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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
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#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))>
#<alt (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))>
#<alt (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))>
#<alt (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))>
#<alt (+.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 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.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 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.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 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.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 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
Calls

96 calls:

TimeVariablePointExpression
178.0ms
n
@-inf
(/ 1 (/ (sqrt (/ k (* n (PI)))) (sqrt 2)))
17.0ms
k
@-inf
(pow (/ (* k 1/2) (* n (PI))) -1/2)
13.0ms
n
@inf
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
1.0ms
n
@-inf
(pow (/ (* k 1/2) (* n (PI))) -1/2)
1.0ms
k
@0
(pow (/ (* k 1/2) (* n (PI))) -1/2)

rewrite1.4s (2.7%)

Algorithm
1×batch-egg-rewrite
Rules
334×prod-diff
247×associate-*r*
243×add-exp-log
243×log1p-expm1-u
243×expm1-log1p-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037466
1629466
27844466
Stop Event
1×node limit
Counts
17 → 712
Calls
Call 1
Inputs
(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 (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))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64)))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (PI.f64) (/.f64 n k))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(/.f64 n k)
(/.f64 k (*.f64 n (PI.f64)))
Outputs
(-.f64 (exp.f64 (log1p.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)))))) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (cbrt.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))))) (pow.f64 (cbrt.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))))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.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))))) #s(literal 2 binary64)) (cbrt.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 (sqrt.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))))) (sqrt.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 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 k #s(literal -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 #s(literal 1 binary64) (+.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)))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (sqrt.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 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) n) (+.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 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 #s(literal 1/2 binary64) 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))))
(pow.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)))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(pow.f64 (cbrt.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))))) #s(literal 3 binary64))
(pow.f64 (pow.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)))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.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))))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (pow.f64 (cbrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal 2 binary64))) (cbrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 (log.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 (exp.f64 (cbrt.f64 (pow.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal 2 binary64)))) (cbrt.f64 (*.f64 (log.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 (exp.f64 (sqrt.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) (sqrt.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(log.f64 (exp.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))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.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)))))))
(cbrt.f64 (pow.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)))) #s(literal 3 binary64)))
(expm1.f64 (log1p.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))))))
(log1p.f64 (expm1.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 (exp.f64 (log1p.f64 (/.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)))) (sqrt.f64 k)))) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)))
(*.f64 (pow.f64 (cbrt.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))))) #s(literal 2 binary64)) (/.f64 (cbrt.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))))) (sqrt.f64 k)))
(*.f64 (pow.f64 (cbrt.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))))) #s(literal 2 binary64)) (*.f64 (cbrt.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))))) (pow.f64 k #s(literal -1/2 binary64))))
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(*.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 k) (cbrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 k n))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (/.f64 k (cbrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 k (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) n) (/.f64 (cbrt.f64 k) (PI.f64)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) (PI.f64)) (/.f64 (cbrt.f64 k) n))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 k) (*.f64 n (PI.f64))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (cbrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(neg.f64 (/.f64 k (*.f64 n (neg.f64 (PI.f64)))))
(neg.f64 (/.f64 (neg.f64 k) (*.f64 n (PI.f64))))
(sqrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 2 binary64)))
(log.f64 (exp.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(log1p.f64 (expm1.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(exp.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1 binary64)))

simplify2.9s (5.9%)

Algorithm
1×egg-herbie
Rules
668×associate-*r*
582×associate-*l*
453×*-commutative
364×associate-*r/
280×associate-*l/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0112440180
1234537945
2768337883
Stop Event
1×node limit
Counts
1016 → 796
Calls
Call 1
Inputs
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))
(*.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)))))
(*.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)))))
(*.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)))))
(*.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)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 #s(literal 1 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 (*.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 (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 #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 (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 (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 (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 (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 (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 (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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
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(/.f64 (*.f64 n (PI.f64)) k)
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(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) (log.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (PI.f64))))
(+.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(+.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(+.f64 (log.f64 (*.f64 #s(literal 2 binary64) n)) (log.f64 (PI.f64)))
(+.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))) #s(literal 1 binary64))
(*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(*.f64 (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (cbrt.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(*.f64 (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(/.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (*.f64 n (PI.f64))) #s(literal 3 binary64))) (+.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64))) (-.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64)))) (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (PI.f64)))))))
(/.f64 (-.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 (*.f64 n (PI.f64))))) (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (PI.f64)))))
(pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 2 binary64)))
(cbrt.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(log1p.f64 (-.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(exp.f64 (*.f64 (log.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))) #s(literal 1 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) #s(literal 2 binary64)))) (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))) (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (*.f64 #s(literal 2 binary64) n)) (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 n k))) #s(literal 1 binary64))
(*.f64 n (/.f64 #s(literal 1 binary64) k))
(*.f64 (/.f64 n k) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 n k))
(*.f64 (cbrt.f64 (/.f64 n k)) (pow.f64 (cbrt.f64 (/.f64 n k)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 n k)) #s(literal 2 binary64)) (cbrt.f64 (/.f64 n k)))
(*.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (/.f64 (cbrt.f64 n) k))
(*.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (*.f64 (cbrt.f64 n) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (/.f64 n k)))
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 n) k))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) k)))
(*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (neg.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) k) n)
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 n (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 n (cbrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (cbrt.f64 n) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 n) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 (/.f64 n k)))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) k))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 n) (cbrt.f64 k)))
(pow.f64 (/.f64 n k) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (/.f64 n k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 n k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 2 binary64))
(pow.f64 (/.f64 k n) #s(literal -1 binary64))
(neg.f64 (/.f64 n (neg.f64 k)))
(neg.f64 (/.f64 (neg.f64 n) k))
(sqrt.f64 (pow.f64 (/.f64 n k) #s(literal 2 binary64)))
(log.f64 (exp.f64 (/.f64 n k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 n k))))
(cbrt.f64 (pow.f64 (/.f64 n k) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (/.f64 n k)))
(log1p.f64 (expm1.f64 (/.f64 n k)))
(exp.f64 (log.f64 (/.f64 n k)))
(exp.f64 (*.f64 (log.f64 (/.f64 n k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 k (PI.f64)) n))) #s(literal 1 binary64))
(*.f64 k (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 k) (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(*.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) n))
(*.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 2 binary64)) (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(*.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) (/.f64 (cbrt.f64 k) (*.f64 n (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) (*.f64 (cbrt.f64 k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(*.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(*.f64 (neg.f64 k) (/.f64 #s(literal 1 binary64) (*.f64 n (neg.f64 (PI.f64)))))
(*.f64 (/.f64 k n) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) k)
(*.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (sqrt.f64 k) n) (/.f64 (sqrt.f64 k) (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 k) (PI.f64)) (/.f64 (sqrt.f64 k) n))
(*.f64 (/.f64 (sqrt.f64 k) #s(literal 1 binary64)) (/.f64 (sqrt.f64 k) (*.f64 n (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (/.f64 (sqrt.f64 k) (cbrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 k n))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (/.f64 k (cbrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 k (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) n) (/.f64 (cbrt.f64 k) (PI.f64)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) (PI.f64)) (/.f64 (cbrt.f64 k) n))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 k) (*.f64 n (PI.f64))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 k #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (cbrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(neg.f64 (/.f64 k (*.f64 n (neg.f64 (PI.f64)))))
(neg.f64 (/.f64 (neg.f64 k) (*.f64 n (PI.f64))))
(sqrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 2 binary64)))
(log.f64 (exp.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(log1p.f64 (expm1.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(exp.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) n)) #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 k #s(literal -1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(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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(/.f64 (/.f64 k n) (PI.f64))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 (*.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))
(/.f64 (/.f64 k n) (PI.f64))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 3 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))
(/.f64 (/.f64 k n) (PI.f64))
(cbrt.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))
(/.f64 (/.f64 k n) (PI.f64))
(expm1.f64 (log1p.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(expm1.f64 (log1p.f64 (/.f64 k (*.f64 n (PI.f64)))))
(expm1.f64 (log1p.f64 (/.f64 (/.f64 k n) (PI.f64))))
(log1p.f64 (expm1.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(/.f64 (*.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))
(/.f64 (/.f64 k n) (PI.f64))
(exp.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(/.f64 (*.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))
(/.f64 (/.f64 k n) (PI.f64))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))
(/.f64 (/.f64 k n) (PI.f64))

eval741.0ms (1.5%)

Compiler

Compiled 16322 to 3450 computations (78.9% saved)

prune725.0ms (1.5%)

Pruning

40 alts after pruning (31 fresh and 9 done)

PrunedKeptTotal
New1000121012
Fresh71926
Picked145
Done055
Total1008401048
Accuracy
100.0%
Counts
1048 → 40
Alt Table
Click to see full alt table
StatusAccuracyProgram
29.4%
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
✓39.4%
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
39.4%
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
39.3%
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 k (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1/2 binary64))
✓99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓96.2%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
48.1%
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
48.1%
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
48.1%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
71.6%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
39.3%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
✓95.9%
(/.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))
38.6%
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal -1/2 binary64)))
36.2%
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
✓48.1%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
38.6%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))))
48.1%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
39.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
39.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
48.1%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)))
48.1%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓38.5%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
48.1%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
✓38.6%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
38.5%
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
38.5%
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k))))
89.9%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
38.7%
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
38.7%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
38.7%
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
38.7%
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
38.7%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
✓38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
36.5%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
✓38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
38.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (fabs.f64 (/.f64 n k)) (PI.f64))))
37.0%
(sqrt.f64 (expm1.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
36.2%
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
31.3%
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
Compiler

Compiled 1242 to 637 computations (48.7% saved)

regimes340.0ms (0.7%)

Counts
65 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 k (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (fabs.f64 (/.f64 n k)) (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #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 (/.f64 k n) (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (expm1.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) k))
(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (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)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))))
(*.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)))))
Outputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Calls

4 calls:

105.0ms
k
83.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
74.0ms
n
51.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%1k
99.6%1n
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes106.0ms (0.2%)

Counts
48 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 k (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (fabs.f64 (/.f64 n k)) (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #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 (/.f64 k n) (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #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 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 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

2 calls:

50.0ms
n
48.0ms
k
Results
AccuracySegmentsBranch
99.6%1k
99.6%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes183.0ms (0.4%)

Counts
46 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 k (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (fabs.f64 (/.f64 n k)) (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #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 (/.f64 k n) (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal 1 binary64))))))
Outputs
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
Calls

2 calls:

81.0ms
n
65.0ms
k
Results
AccuracySegmentsBranch
99.3%2k
89.9%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes205.0ms (0.4%)

Counts
44 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 k (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (fabs.f64 (/.f64 n k)) (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #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 (/.f64 k n) (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
Outputs
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
Calls

1 calls:

20.0ms
k
Results
AccuracySegmentsBranch
99.2%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes106.0ms (0.2%)

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

2 calls:

61.0ms
n
38.0ms
k
Results
AccuracySegmentsBranch
53.1%3n
56.3%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes54.0ms (0.1%)

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

1 calls:

32.0ms
k
Results
AccuracySegmentsBranch
56.3%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes36.0ms (0.1%)

Counts
34 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 k (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (fabs.f64 (/.f64 n k)) (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #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 (/.f64 k n) (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
Outputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
Calls

1 calls:

31.0ms
k
Results
AccuracySegmentsBranch
56.3%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes102.0ms (0.2%)

Counts
33 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 k (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (fabs.f64 (/.f64 n k)) (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #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 (/.f64 k n) (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
Outputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
Calls

2 calls:

46.0ms
k
27.0ms
n
Results
AccuracySegmentsBranch
48.1%1n
48.1%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes64.0ms (0.1%)

Counts
29 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 k (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (fabs.f64 (/.f64 n k)) (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #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 (/.f64 k n) (PI.f64))))
Outputs
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
Calls

2 calls:

48.0ms
n
13.0ms
k
Results
AccuracySegmentsBranch
39.4%1n
39.4%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes21.0ms (0%)

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

2 calls:

13.0ms
n
6.0ms
k
Results
AccuracySegmentsBranch
39.4%1k
39.4%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes29.0ms (0.1%)

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

2 calls:

23.0ms
k
5.0ms
n
Results
AccuracySegmentsBranch
38.7%1k
38.7%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

2 calls:

2.0ms
k
2.0ms
n
Results
AccuracySegmentsBranch
38.7%1k
38.7%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch41.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
38.0ms
1.8441052236173596e-51
2.898762023043566e-51
Results
34.0ms64×0valid
Compiler

Compiled 143 to 117 computations (18.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 30.0ms
ival-pow: 19.0ms (63.3% of total)
ival-mult: 7.0ms (23.3% of total)
ival-div: 2.0ms (6.7% of total)
ival-sub: 1.0ms (3.3% of total)
ival-sqrt: 1.0ms (3.3% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch80.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
76.0ms
1.565330076171216e-58
5.449176100885495e-57
Results
20.0ms112×0valid
Compiler

Compiled 226 to 185 computations (18.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-mult: 4.0ms (28.2% of total)
ival-pow: 4.0ms (28.2% of total)
ival-div: 3.0ms (21.2% of total)
ival-pi: 1.0ms (7.1% of total)
ival-sub: 1.0ms (7.1% of total)
ival-sqrt: 1.0ms (7.1% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch48.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
45.0ms
4.684138773410299e+80
6.945679042407848e+80
Results
26.0ms48×0valid
Compiler

Compiled 107 to 89 computations (16.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-pow: 3.0ms (40.6% of total)
ival-mult: 2.0ms (27% of total)
ival-div: 1.0ms (13.5% of total)
ival-sqrt: 1.0ms (13.5% of total)
ival-pi: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch33.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
31.0ms
4.684138773410299e+80
6.945679042407848e+80
Results
28.0ms48×0valid
Compiler

Compiled 107 to 89 computations (16.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-mult: 18.0ms (72% of total)
ival-pow: 4.0ms (16% of total)
ival-sub: 1.0ms (4% of total)
ival-div: 1.0ms (4% of total)
ival-sqrt: 1.0ms (4% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch33.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
32.0ms
4.684138773410299e+80
6.945679042407848e+80
Results
29.0ms48×0valid
0.0ms1×0unsamplable
Compiler

Compiled 101 to 83 computations (17.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 26.0ms
ival-pow: 22.0ms (83.1% of total)
ival-div: 1.0ms (3.8% of total)
ival-mult: 1.0ms (3.8% of total)
ival-sqrt: 1.0ms (3.8% of total)
ival-pi: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify34.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
084743
1110743
2119743
3125743
4129743
5130743
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (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 2358995333375681/842498333348457493583344221469363458551160763204392890034487820288 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 4152090602229203/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 479999999999999958002810683177288248212320452201590956112995331557106341073911808 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(if (<=.f64 k #s(literal 499999999999999960640939947832891370967751624529591925904999112061532074214948864 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(if (<=.f64 k #s(literal 499999999999999960640939947832891370967751624529591925904999112061532074214948864 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
Outputs
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (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 2358995333375681/842498333348457493583344221469363458551160763204392890034487820288 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 2358995333375681/842498333348457493583344221469363458551160763204392890034487820288 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 4152090602229203/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 4152090602229203/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 479999999999999958002810683177288248212320452201590956112995331557106341073911808 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(if (<=.f64 k #s(literal 499999999999999960640939947832891370967751624529591925904999112061532074214948864 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(if (<=.f64 k #s(literal 499999999999999960640939947832891370967751624529591925904999112061532074214948864 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(if (<=.f64 k #s(literal 499999999999999960640939947832891370967751624529591925904999112061532074214948864 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(if (<=.f64 k #s(literal 499999999999999960640939947832891370967751624529591925904999112061532074214948864 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 n (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))

soundness7.6s (15.2%)

Rules
724×fma-define
704×fma-define
513×associate-*r*
487×associate-*l*
486×exp-prod
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
037466
1629466
27844466
0114847848
1245346452
2609945874
036497
1588497
27645497
059819152
1121017098
2421016476
095226802
1198125714
2702925228
045451
1830443
039438
196380
2211380
3410364
4686352
51171352
61433352
71698352
82017352
92060352
102088352
112099352
122101352
Stop Event
1×fuel
1×saturated
1×node limit
1×node limit
1×node limit
1×node limit
1×node limit
1×node limit
Compiler

Compiled 1691 to 653 computations (61.4% saved)

preprocess270.0ms (0.5%)

Compiler

Compiled 448 to 170 computations (62.1% saved)

end0.0ms (0%)

Profiling

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