Migdal et al, Equation (51)

Time bar (total: 21.2s)

analyze205.0ms (1%)

Algorithm
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 16 computations (15.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 147.0ms
Operation ival-pow, time spent: 96.0ms, 65.0% of total-time
Operation ival-mult, time spent: 20.0ms, 14.0% of total-time
Operation ival-div, time spent: 14.0ms, 10.0% of total-time
Operation ival-sqrt, time spent: 7.0ms, 5.0% of total-time
Operation ival-sub, time spent: 5.0ms, 3.0% of total-time
Operation ival-pi, time spent: 4.0ms, 3.0% of total-time
Operation const, time spent: 2.0ms, 1.0% of total-time

sample8.5s (40.1%)

Results
1.5s6212×0valid
4.4s3790×5exit
656.0ms2043×0infinite
681.0ms1929×1invalid
71.0ms559×0invalid
45.0ms240×0unsamplable
0.0ms0valid
Precisions
Click to see histograms. Total time spent on operations: 5.0s
Operation ival-pow, time spent: 1.7s, 33.0% of total-time
Operation ival-mult, time spent: 1.2s, 23.0% of total-time
Operation ival-div, time spent: 663.0ms, 13.0% of total-time
Operation backward-pass, time spent: 577.0ms, 11.0% of total-time
Operation ival-sqrt, time spent: 406.0ms, 8.0% of total-time
Operation ival-sub, time spent: 303.0ms, 6.0% of total-time
Operation ival-pi, time spent: 182.0ms, 4.0% of total-time
Operation const, time spent: 103.0ms, 2.0% of total-time
Bogosity

preprocess433.0ms (2%)

Algorithm
egg-herbie
Rules
465×fma-define
240×fma-neg
124×associate-*r*
80×associate-*l*
74×sub-neg
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
4209(2.3350965825879678e-297 5.619752049363708e+231)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
Iterations

Useful iterations: 4 (0.0ms)

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

Compiled 132 to 93 computations (29.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 112.0ms
Operation ival-pow, time spent: 39.0ms, 35.0% of total-time
Operation ival-mult, time spent: 30.0ms, 27.0% of total-time
Operation ival-div, time spent: 20.0ms, 18.0% of total-time
Operation ival-sub, time spent: 12.0ms, 11.0% of total-time
Operation ival-sqrt, time spent: 5.0ms, 4.0% of total-time
Operation const, time spent: 4.0ms, 4.0% of total-time
Operation ival-pi, time spent: 2.0ms, 2.0% of total-time

eval1.0ms (0%)

Compiler

Compiled 59 to 38 computations (35.6% saved)

prune2.0ms (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))
99.4%
(*.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 28 computations (17.6% saved)

localize192.0ms (0.9%)

Localize:

Found 7 expressions with local error:

NewAccuracyProgram
99.8%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
99.7%
(/.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))
99.6%
(*.f64 (PI.f64) n)
99.8%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
99.7%
(*.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))))
99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
Compiler

Compiled 105 to 65 computations (38.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 98.0ms
Operation ival-pow, time spent: 39.0ms, 40.0% of total-time
Operation ival-mult, time spent: 23.0ms, 23.0% of total-time
Operation ival-div, time spent: 18.0ms, 18.0% of total-time
Operation ival-sub, time spent: 10.0ms, 10.0% of total-time
Operation const, time spent: 3.0ms, 3.0% of total-time
Operation ival-pi, time spent: 2.0ms, 2.0% of total-time
Operation ival-sqrt, time spent: 2.0ms, 2.0% of total-time

series126.0ms (0.6%)

Counts
7 → 132
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))))>
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)))))>
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#<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))))>
Calls

33 calls:

TimeVariablePointExpression
67.0ms
n
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
26.0ms
n
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
7.0ms
n
@inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
4.0ms
k
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
2.0ms
k
@0
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))

rewrite289.0ms (1.4%)

Algorithm
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
026226
1427222
24798222
Stop Event
node limit
Counts
7 → 198
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))))
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))))
(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 (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 (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 (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 (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))))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.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)))) (cbrt.f64 k)) (cbrt.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 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(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 (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)) 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 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 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)) (pow.f64 (pow.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)) (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 (*.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))
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(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 (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)) 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))))
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(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))))
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(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 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
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(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
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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)))

simplify244.0ms (1.2%)

Algorithm
egg-herbie
Rules
644×times-frac
588×fma-define
331×associate-*r*
305×associate-*r/
278×associate-*l*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
045517552
198516254
2312814844
Stop Event
node limit
Counts
330 → 300
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)))
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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)))
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 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 (+.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 k (*.f64 n (PI.f64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) k)
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (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 #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 (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (pow.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) #s(literal 2 binary64))) (sqrt.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 -1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (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 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (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 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 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 (*.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 (*.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 (*.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 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 #s(literal 1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64))))) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (fma.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))))) (*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (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 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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))))
(*.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 #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 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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))))
(*.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 #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 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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))))
(*.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 #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 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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))))
(*.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 #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)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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))))
(*.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 #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)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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))))
(*.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 #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)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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))))
(*.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 #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)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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))))
(*.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 #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)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 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))))
(*.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 #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)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
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(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))))
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(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(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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(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(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 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (sqrt.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 (sqrt.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 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(pow.f64 (sqrt.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))))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64))))
(sqrt.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 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(log.f64 (exp.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 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
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(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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(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(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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(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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(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp.f64 (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))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (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)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))

eval146.0ms (0.7%)

Compiler

Compiled 6729 to 4479 computations (33.4% saved)

prune251.0ms (1.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New28911300
Fresh000
Picked022
Done000
Total28913302
Accuracy
100.0%
Counts
302 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.2%
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
98.7%
(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))
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))
99.7%
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
99.7%
(/.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)))))
99.5%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
74.7%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
99.4%
(*.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))))
50.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
36.7%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
36.7%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
36.7%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
85.7%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
Compiler

Compiled 396 to 320 computations (19.2% saved)

localize1.8s (8.7%)

Localize:

Found 20 expressions with local error:

NewAccuracyProgram
99.7%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
99.7%
(*.f64 (PI.f64) n)
99.6%
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
76.2%
(PI.f64)
99.8%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
99.7%
(*.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)))
99.7%
(*.f64 (PI.f64) n)
76.2%
(PI.f64)
99.7%
(*.f64 n (PI.f64))
99.5%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
85.9%
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
76.2%
(PI.f64)
99.7%
(/.f64 (PI.f64) k)
99.5%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
85.9%
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
76.2%
(PI.f64)
99.9%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))
99.8%
(/.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)))))
99.7%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
76.2%
(PI.f64)
Compiler

Compiled 244 to 134 computations (45.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.5s
Operation ival-pow, time spent: 1.1s, 74.0% of total-time
Operation ival-mult, time spent: 257.0ms, 17.0% of total-time
Operation ival-sqrt, time spent: 68.0ms, 4.0% of total-time
Operation ival-div, time spent: 26.0ms, 2.0% of total-time
Operation ival-sub, time spent: 24.0ms, 2.0% of total-time
Operation const, time spent: 16.0ms, 1.0% of total-time
Operation ival-pi, time spent: 4.0ms, 0.0% of total-time

series124.0ms (0.6%)

Counts
17 → 196
Calls
Call 1
Inputs
#<alt (PI.f64)>
#<alt (/.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)))))>
#<alt (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))>
#<alt (PI.f64)>
#<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 (PI.f64)>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 n (PI.f64))>
#<alt (PI.f64)>
#<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 (PI.f64)>
#<alt (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))>
#<alt (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))>
Outputs
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))>
#<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 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (+.f64 (*.f64 #s(literal -1/16 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 1/48 binary64) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #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)))>
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#<alt (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (*.f64 #s(literal 1/4 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 (exp.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (exp.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (exp.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>
Calls

63 calls:

TimeVariablePointExpression
20.0ms
k
@0
(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
15.0ms
n
@0
(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
15.0ms
k
@inf
(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
13.0ms
k
@-inf
(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
5.0ms
n
@inf
(/ (sqrt (* (* 2 (PI)) n)) (* (sqrt k) (pow (* (* 2 (PI)) n) (* k 1/2))))

rewrite147.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
294×log1p-expm1-u
294×expm1-log1p-u
293×pow1
289×add-cube-cbrt
286×associate-*r*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
043453
1762424
Stop Event
node limit
Counts
17 → 400
Calls
Call 1
Inputs
(PI.f64)
(/.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)))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))
(PI.f64)
(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)
(PI.f64)
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 n (PI.f64))
(PI.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)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(PI.f64)
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
Outputs
(-.f64 (exp.f64 (log1p.f64 (PI.f64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.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))
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(*.f64 (/.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 k #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal 1/8 binary64))) (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/8 binary64))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/8 binary64))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal 1/8 binary64))))
(*.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (cbrt.f64 (pow.f64 k #s(literal 1/4 binary64)))))
(pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (sqrt.f64 k)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (pow.f64 k #s(literal 1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(neg.f64 (/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 k #s(literal 1/4 binary64)))))
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(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(fabs.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(exp.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 1 binary64)))

simplify339.0ms (1.6%)

Algorithm
egg-herbie
Rules
646×associate-*r*
540×associate-*l*
462×*-commutative
262×exp-prod
213×fma-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
089729182
1211027744
2667626617
Stop Event
node limit
Counts
596 → 573
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
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(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
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(*.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))
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(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
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(*.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (cbrt.f64 (pow.f64 k #s(literal 1/4 binary64)))))
(pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (sqrt.f64 k)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (pow.f64 k #s(literal 1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(neg.f64 (/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 k #s(literal 1/4 binary64)))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(fabs.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(exp.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 1 binary64)))
Outputs
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) k)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
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(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (pow.f64 k #s(literal 1/8 binary64))) #s(literal 2 binary64))
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(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)))
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(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 1 binary64)))
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(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal -1/4 binary64)))))

eval334.0ms (1.6%)

Compiler

Compiled 17009 to 11552 computations (32.1% saved)

prune134.0ms (0.6%)

Pruning

17 alts after pruning (13 fresh and 4 done)

PrunedKeptTotal
New76111772
Fresh426
Picked235
Done112
Total76817785
Accuracy
100.0%
Counts
785 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
36.7%
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
36.7%
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 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))
99.5%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
50.6%
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
38.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
50.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
50.7%
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
36.7%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
36.7%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
36.7%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
36.7%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
85.7%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
85.7%
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)))
85.9%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
36.9%
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
Compiler

Compiled 397 to 325 computations (18.1% saved)

localize1.2s (5.7%)

Localize:

Found 20 expressions with local error:

NewAccuracyProgram
99.7%
(*.f64 (PI.f64) n)
99.6%
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
99.5%
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
76.2%
(PI.f64)
99.7%
(*.f64 n (PI.f64))
99.4%
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
85.7%
(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64))
76.2%
(PI.f64)
99.6%
(*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))
99.5%
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
85.9%
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))))
76.2%
(PI.f64)
99.8%
(*.f64 n (/.f64 (PI.f64) k))
99.7%
(/.f64 (PI.f64) k)
85.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
76.2%
(PI.f64)
99.8%
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
99.7%
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
85.9%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
76.2%
(PI.f64)
Compiler

Compiled 216 to 110 computations (49.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 890.0ms
Operation ival-pow, time spent: 584.0ms, 66.0% of total-time
Operation ival-mult, time spent: 164.0ms, 18.0% of total-time
Operation ival-sqrt, time spent: 66.0ms, 7.0% of total-time
Operation ival-div, time spent: 62.0ms, 7.0% of total-time
Operation const, time spent: 11.0ms, 1.0% of total-time
Operation ival-pi, time spent: 3.0ms, 0.0% of total-time

series260.0ms (1.2%)

Counts
12 → 264
Calls
Call 1
Inputs
#<alt (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))>
#<alt (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))>
#<alt (*.f64 n (/.f64 (PI.f64) k))>
#<alt (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))>
#<alt (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64))>
#<alt (pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))>
#<alt (*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))>
Outputs
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))) k)>
#<alt (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) k))))))))))))) k)>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<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 (PI.f64) k)>
#<alt (/.f64 (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) (*.f64 k (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) k)>
#<alt (/.f64 (+.f64 (PI.f64) (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) k)>
#<alt (/.f64 (+.f64 (PI.f64) (*.f64 k (-.f64 (*.f64 k (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/6 binary64) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)))))))) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) k)>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))>
#<alt (/.f64 (PI.f64) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))>
#<alt (*.f64 (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)))))>
#<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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<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))>
Calls

66 calls:

TimeVariablePointExpression
143.0ms
k
@0
(pow (/ (* 2 (* n (PI))) k) 1/4)
19.0ms
n
@-inf
(pow (/ (* 2 (* n (PI))) k) 1/4)
18.0ms
k
@-inf
(pow (/ (* 2 (* n (PI))) k) 1/4)
18.0ms
n
@0
(pow (/ (* 2 (* n (PI))) k) 1/4)
10.0ms
n
@inf
(pow (/ (* 2 (* n (PI))) k) 1/4)

rewrite253.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
464×log1p-expm1-u
273×associate-*r*
220×expm1-log1p-u
219×pow1
218×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040365
1709365
27245365
Stop Event
node limit
Counts
12 → 477
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
(*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 n (/.f64 (PI.f64) k))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))
(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))) (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))))
(*.f64 (sqrt.f64 n) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) n) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(cbrt.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(log1p.f64 (expm1.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(exp.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) #s(literal 1 binary64))
(*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))
(*.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) #s(literal 1 binary64))
(*.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 (PI.f64) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (PI.f64)) (*.f64 k (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))
(*.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))) (pow.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))) #s(literal 2 binary64)) (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) (*.f64 k (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k) (neg.f64 k))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) (PI.f64))
(*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)) (/.f64 (PI.f64) k))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 (*.f64 k (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))) #s(literal 2 binary64))) (/.f64 (PI.f64) (cbrt.f64 (*.f64 k (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) (/.f64 (PI.f64) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (PI.f64)) (*.f64 k (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) (*.f64 k (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) k)))
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(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (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 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(*.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/8 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(*.f64 (cbrt.f64 #s(literal 2 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/8 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal -2 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(fabs.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal -2 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(fabs.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 k)) (/.f64 (sqrt.f64 n) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(fabs.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 1 binary64)))

simplify367.0ms (1.7%)

Algorithm
egg-herbie
Rules
598×associate-*r*
531×associate-*l*
420×exp-prod
398×*-commutative
310×cube-prod
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
085030874
1187329947
2709529715
Stop Event
node limit
Counts
741 → 466
Calls
Call 1
Inputs
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(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) #s(literal -2 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(fabs.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 n) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 k)) (/.f64 (sqrt.f64 n) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(fabs.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 1 binary64)))
Outputs
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) (*.f64 k (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (/.f64 (PI.f64) k) (*.f64 (pow.f64 n k) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) (pow.f64 (exp.f64 k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n (pow.f64 (exp.f64 k) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (*.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)) (*.f64 k (exp.f64 (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
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(*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (fabs.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (fabs.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 k)) (/.f64 (sqrt.f64 n) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 k))) (cbrt.f64 (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))))
(/.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))
(*.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 3 binary64))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/4 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(fabs.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 1 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))

eval528.0ms (2.5%)

Compiler

Compiled 17283 to 10432 computations (39.6% saved)

prune300.0ms (1.4%)

Pruning

27 alts after pruning (22 fresh and 5 done)

PrunedKeptTotal
New1028171045
Fresh358
Picked325
Done134
Total1035271062
Accuracy
100.0%
Counts
1062 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
36.7%
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
26.2%
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
36.7%
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
24.0%
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 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))
50.7%
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
38.2%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
50.7%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
38.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
99.5%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
50.6%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
50.7%
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
50.7%
(*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
36.7%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
36.7%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
50.6%
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
50.7%
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
85.7%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
85.7%
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)))
85.9%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
36.9%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
36.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
36.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
36.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
34.5%
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
27.9%
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
Compiler

Compiled 611 to 504 computations (17.5% saved)

localize375.0ms (1.8%)

Localize:

Found 20 expressions with local error:

NewAccuracyProgram
99.7%
(*.f64 n (/.f64 (PI.f64) k))
99.7%
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
99.7%
(/.f64 (PI.f64) k)
44.9%
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
99.7%
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
99.7%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64))
99.7%
(/.f64 (PI.f64) k)
54.4%
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
99.7%
(/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
99.6%
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
74.4%
(sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
100.0%
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
99.7%
(/.f64 n (/.f64 k (PI.f64)))
99.5%
(/.f64 k (PI.f64))
74.2%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
99.8%
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)
99.8%
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))
99.6%
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
85.9%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
Compiler

Compiled 196 to 100 computations (49% saved)

Precisions
Click to see histograms. Total time spent on operations: 169.0ms
Operation ival-pow, time spent: 67.0ms, 40.0% of total-time
Operation ival-mult, time spent: 61.0ms, 36.0% of total-time
Operation ival-div, time spent: 16.0ms, 9.0% of total-time
Operation ival-sqrt, time spent: 10.0ms, 6.0% of total-time
Operation ival-sub, time spent: 6.0ms, 4.0% of total-time
Operation const, time spent: 5.0ms, 3.0% of total-time
Operation ival-cbrt, time spent: 2.0ms, 1.0% of total-time
Operation ival-pi, time spent: 1.0ms, 1.0% of total-time

series93.0ms (0.4%)

Counts
17 → 360
Calls
Call 1
Inputs
#<alt (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))>
#<alt (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))>
#<alt (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))>
#<alt (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))>
#<alt (/.f64 k (PI.f64))>
#<alt (/.f64 n (/.f64 k (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))>
#<alt (sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))>
#<alt (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))>
#<alt (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))>
#<alt (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))>
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64))>
#<alt (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))>
#<alt (pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))>
#<alt (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))>
Outputs
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
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#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (pow.f64 k #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -8 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))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
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#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 2 binary64)))>
Calls

93 calls:

TimeVariablePointExpression
16.0ms
n
@0
(pow (* (pow (* n (/ (PI) k)) 2) 4) 1/4)
6.0ms
k
@0
(pow (* (pow (* n (/ (PI) k)) 2) 4) 1/4)
4.0ms
n
@0
(pow (* n (* 2 (/ (PI) k))) 3/2)
3.0ms
k
@-inf
(/ 1 (sqrt (/ k (* (* n 2) (PI)))))
3.0ms
n
@0
(pow (* n (/ (PI) k)) 2)

rewrite168.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
251×log1p-expm1-u
251×expm1-log1p-u
246×pow1
243×add-exp-log
243×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037486
1622486
Stop Event
node limit
Counts
17 → 698
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(/.f64 k (PI.f64))
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(/.f64 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.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))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.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 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64))) (sqrt.f64 (cbrt.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) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.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))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) #s(literal 1 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 3 binary64))
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(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 2 binary64))
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(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1 binary64)))

simplify476.0ms (2.2%)

Algorithm
egg-herbie
Rules
724×times-frac
693×fma-define
425×associate-*r/
388×associate-*l/
339×associate-/l*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
011338589975881
124698589974032
274188589974032
Stop Event
node limit
Counts
1058 → 763
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
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(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
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(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
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(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
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(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.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 binary64) k)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.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 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 binary64) k)))
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(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
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(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
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(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))
(/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k)
(/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k)
(/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k)
(/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k)
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(/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k)
(/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k)
(/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k)
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(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 n)) (/.f64 (neg.f64 k) (PI.f64)))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))))
(/.f64 (*.f64 (neg.f64 n) #s(literal 2 binary64)) (/.f64 (neg.f64 k) (PI.f64)))
(/.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (cbrt.f64 k))
(/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (/.f64 k (PI.f64))))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))) #s(literal -2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 2/3 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 4 binary64)) #s(literal 16 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)))
(fabs.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(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) #s(literal 2 binary64)) k)))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 k (PI.f64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(exp.f64 (log.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 1 binary64)))
(exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (log.f64 k)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) (cbrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(*.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) (cbrt.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 4 binary64)) #s(literal 16 binary64))) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(*.f64 (pow.f64 (pow.f64 n #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3/4 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3/4 binary64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 n #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 3/2 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))))
(/.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))) (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(fabs.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3/2 binary64))) #s(literal 1/3 binary64)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 n (*.f64 (/.f64 (PI.f64) k) (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))
(*.f64 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (/.f64 (PI.f64) k) (*.f64 n (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)) (pow.f64 n #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 4 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 4 binary64))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (/.f64 n k) (*.f64 (PI.f64) (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (pow.f64 (/.f64 n k) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (*.f64 (/.f64 n k) (/.f64 n k)) (pow.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) n) (/.f64 (PI.f64) k))
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (/.f64 (PI.f64) k)) n)
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64))) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (/.f64 n k)) (PI.f64))
(/.f64 n (*.f64 (/.f64 k (PI.f64)) (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 n (*.f64 (/.f64 k (*.f64 (PI.f64) n)) (/.f64 k (PI.f64))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (PI.f64) (/.f64 n k)) (/.f64 k (*.f64 (PI.f64) n)))
(/.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (/.f64 k (PI.f64)) #s(literal 2 binary64)))
(/.f64 (neg.f64 n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) (/.f64 (neg.f64 k) (PI.f64))))
(/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k))
(/.f64 (*.f64 (neg.f64 n) (neg.f64 n)) (*.f64 (/.f64 (neg.f64 k) (PI.f64)) (/.f64 (neg.f64 k) (PI.f64))))
(/.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 2 binary64)))
(/.f64 (*.f64 n (neg.f64 n)) (*.f64 (/.f64 k (PI.f64)) (/.f64 (neg.f64 k) (PI.f64))))
(/.f64 (*.f64 n (*.f64 (PI.f64) n)) (*.f64 (/.f64 k (PI.f64)) k))
(/.f64 (*.f64 (neg.f64 n) n) (*.f64 (/.f64 (neg.f64 k) (PI.f64)) (/.f64 k (PI.f64))))
(/.f64 (*.f64 (neg.f64 n) #s(literal 1 binary64)) (*.f64 (/.f64 (neg.f64 k) (PI.f64)) (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (neg.f64 n) (*.f64 (PI.f64) n)) (*.f64 (/.f64 (neg.f64 k) (PI.f64)) k))
(/.f64 (*.f64 (*.f64 (PI.f64) n) n) (*.f64 k (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) (*.f64 k (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (*.f64 (PI.f64) n) (neg.f64 n)) (*.f64 k (/.f64 (neg.f64 k) (PI.f64))))
(/.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) n) (/.f64 k (PI.f64)))
(/.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 n k))) (/.f64 k (PI.f64)))
(/.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (neg.f64 n)) (/.f64 (neg.f64 k) (PI.f64)))
(/.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 (PI.f64) n)) k)
(/.f64 (*.f64 (neg.f64 n) (*.f64 (PI.f64) (/.f64 n k))) (/.f64 (neg.f64 k) (PI.f64)))
(/.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) (/.f64 n k))) k)
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 4 binary64)))
(log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1 binary64)))
Outputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.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 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.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 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.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 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)) k))
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(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)) (pow.f64 n #s(literal 2 binary64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 4 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 4 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 4 binary64))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 4 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 4 binary64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (/.f64 n k) (*.f64 (PI.f64) (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (pow.f64 (/.f64 n k) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (*.f64 (/.f64 n k) (/.f64 n k)) (pow.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) n) (/.f64 (PI.f64) k))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (/.f64 (PI.f64) k)) n)
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64))) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (/.f64 n k)) (PI.f64))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 n (*.f64 (/.f64 k (PI.f64)) (/.f64 k (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 n (*.f64 (/.f64 k (*.f64 (PI.f64) n)) (/.f64 k (PI.f64))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) (/.f64 n k)) (/.f64 k (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (pow.f64 n #s(literal 2 binary64)) (pow.f64 (/.f64 k (PI.f64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (neg.f64 n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) (/.f64 (neg.f64 k) (PI.f64))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 n) (neg.f64 n)) (*.f64 (/.f64 (neg.f64 k) (PI.f64)) (/.f64 (neg.f64 k) (PI.f64))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 2 binary64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 n (neg.f64 n)) (*.f64 (/.f64 k (PI.f64)) (/.f64 (neg.f64 k) (PI.f64))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 n (*.f64 (PI.f64) n)) (*.f64 (/.f64 k (PI.f64)) k))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 n) n) (*.f64 (/.f64 (neg.f64 k) (PI.f64)) (/.f64 k (PI.f64))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 n) #s(literal 1 binary64)) (*.f64 (/.f64 (neg.f64 k) (PI.f64)) (/.f64 k (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 n) (*.f64 (PI.f64) n)) (*.f64 (/.f64 (neg.f64 k) (PI.f64)) k))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (PI.f64) n) n) (*.f64 k (/.f64 k (PI.f64))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64)) (*.f64 k (/.f64 k (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (PI.f64) n) (neg.f64 n)) (*.f64 k (/.f64 (neg.f64 k) (PI.f64))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) n) (/.f64 k (PI.f64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 n k))) (/.f64 k (PI.f64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (neg.f64 n)) (/.f64 (neg.f64 k) (PI.f64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 (PI.f64) n)) k)
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 n) (*.f64 (PI.f64) (/.f64 n k))) (/.f64 (neg.f64 k) (PI.f64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) (/.f64 n k))) k)
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 4 binary64)))
(sqrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 4 binary64)))
(log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 n #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))

eval316.0ms (1.5%)

Compiler

Compiled 15287 to 9327 computations (39% saved)

prune198.0ms (0.9%)

Pruning

41 alts after pruning (35 fresh and 6 done)

PrunedKeptTotal
New91628944
Fresh10717
Picked235
Done235
Total93041971
Accuracy
100.0%
Counts
971 → 41
Alt Table
Click to see full alt table
StatusAccuracyProgram
26.2%
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
36.7%
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
38.3%
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
17.9%
(pow.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) n) n) (*.f64 k (/.f64 k (PI.f64)))) #s(literal 4 binary64)) #s(literal 1/4 binary64))
25.8%
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
50.7%
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
36.6%
(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
50.7%
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
38.2%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
38.1%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) n)) (sqrt.f64 (PI.f64))))
36.8%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
50.6%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
38.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
87.1%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))))
38.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) k)))
38.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64))) (/.f64 k (PI.f64)))))
38.1%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
99.5%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
50.7%
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
36.6%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
50.7%
(*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
36.7%
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
36.7%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
50.6%
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
50.7%
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
85.7%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
36.8%
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
36.8%
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))
36.8%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
38.7%
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal 1 binary64))))
85.9%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)))))
36.9%
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
36.8%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
36.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
39.1%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
36.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
36.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) (PI.f64))))))
36.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
34.5%
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
27.9%
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
Compiler

Compiled 1293 to 904 computations (30.1% saved)

regimes155.0ms (0.7%)

Counts
69 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.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 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64))) (/.f64 k (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) k)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) n) n) (*.f64 k (/.f64 k (PI.f64)))) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) 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 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #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)))))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) n)) (sqrt.f64 (PI.f64))))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 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 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #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))
(*.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)))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) 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 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) (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))))
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(/.f64 (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 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(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))
Outputs
(/.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)))))
Calls

4 calls:

46.0ms
k
44.0ms
n
38.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
21.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.7%1k
99.7%1n
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 25 computations (19.4% saved)

regimes144.0ms (0.7%)

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

4 calls:

38.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
37.0ms
n
37.0ms
k
25.0ms
(*.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 25 computations (19.4% saved)

regimes363.0ms (1.7%)

Counts
56 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.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 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64))) (/.f64 k (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) k)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) n) n) (*.f64 k (/.f64 k (PI.f64)))) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) 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 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #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)))))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) n)) (sqrt.f64 (PI.f64))))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 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 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))))
Outputs
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
Calls

2 calls:

254.0ms
n
104.0ms
k
Results
AccuracySegmentsBranch
99.6%2k
89.5%2n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes136.0ms (0.6%)

Counts
52 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.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 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64))) (/.f64 k (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) k)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) n) n) (*.f64 k (/.f64 k (PI.f64)))) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) 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 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) #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)))))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) n)) (sqrt.f64 (PI.f64))))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
Outputs
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.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

2 calls:

77.0ms
n
54.0ms
k
Results
AccuracySegmentsBranch
56.5%3n
61.6%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes42.0ms (0.2%)

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

1 calls:

39.0ms
k
Results
AccuracySegmentsBranch
56.3%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes44.0ms (0.2%)

Counts
24 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.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 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64))) (/.f64 k (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) k)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (*.f64 (PI.f64) n) n) (*.f64 k (/.f64 k (PI.f64)))) #s(literal 4 binary64)) #s(literal 1/4 binary64))
Outputs
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
Calls

2 calls:

27.0ms
k
15.0ms
n
Results
AccuracySegmentsBranch
38.3%1n
43.9%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes32.0ms (0.1%)

Counts
22 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.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 k (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64))) (/.f64 k (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 n #s(literal 2 binary64))) k)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))))
Outputs
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
Calls

2 calls:

17.0ms
k
14.0ms
n
Results
AccuracySegmentsBranch
38.3%1n
38.3%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes17.0ms (0.1%)

Counts
9 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))
Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
Calls

2 calls:

9.0ms
k
7.0ms
n
Results
AccuracySegmentsBranch
36.9%1k
36.9%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

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

2 calls:

2.0ms
k
2.0ms
n
Results
AccuracySegmentsBranch
36.9%1k
36.9%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch31.0ms (0.1%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
31.0ms
1.2664053336273315e-53
5.951965872330841e-50
Results
24.0ms127×0valid
0.0ms0valid
Compiler

Compiled 239 to 195 computations (18.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
Operation ival-mult, time spent: 3.0ms, 27.0% of total-time
Operation ival-pow, time spent: 3.0ms, 27.0% of total-time
Operation ival-div, time spent: 2.0ms, 18.0% of total-time
Operation ival-pi, time spent: 1.0ms, 9.0% of total-time
Operation ival-sub, time spent: 1.0ms, 9.0% of total-time
Operation ival-sqrt, time spent: 1.0ms, 9.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time
Operation backward-pass, time spent: 0.0ms, 0.0% of total-time

bsearch27.0ms (0.1%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
27.0ms
1.6959903488647088e+41
5.3879268243794704e+42
Results
11.0ms61×0infinite
12.0ms50×0valid
0.0ms0valid
Compiler

Compiled 205 to 173 computations (15.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
Operation ival-pow, time spent: 5.0ms, 45.0% of total-time
Operation ival-div, time spent: 2.0ms, 18.0% of total-time
Operation ival-mult, time spent: 2.0ms, 18.0% of total-time
Operation ival-sub, time spent: 1.0ms, 9.0% of total-time
Operation ival-sqrt, time spent: 1.0ms, 9.0% of total-time
Operation ival-pi, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time
Operation backward-pass, time spent: 0.0ms, 0.0% of total-time

bsearch21.0ms (0.1%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
21.0ms
2.23973154798128e+169
3.3927307185680845e+169
Results
6.0ms34×0infinite
12.0ms29×0valid
0.0ms0valid
Compiler

Compiled 143 to 107 computations (25.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
Operation ival-mult, time spent: 8.0ms, 60.0% of total-time
Operation ival-pow, time spent: 3.0ms, 23.0% of total-time
Operation ival-div, time spent: 1.0ms, 8.0% of total-time
Operation ival-sqrt, time spent: 1.0ms, 8.0% of total-time
Operation ival-pi, time spent: 0.0ms, 0.0% of total-time
Operation ival-sub, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time
Operation backward-pass, time spent: 0.0ms, 0.0% of total-time

bsearch22.0ms (0.1%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
22.0ms
2.2337624730308243e+168
2.23973154798128e+169
Results
9.0ms53×0valid
8.0ms42×0infinite
0.0ms0infinite
Compiler

Compiled 203 to 151 computations (25.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
Operation ival-pow, time spent: 4.0ms, 43.0% of total-time
Operation ival-mult, time spent: 2.0ms, 21.0% of total-time
Operation ival-sub, time spent: 1.0ms, 11.0% of total-time
Operation ival-div, time spent: 1.0ms, 11.0% of total-time
Operation ival-sqrt, time spent: 1.0ms, 11.0% of total-time
Operation ival-pi, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time
Operation backward-pass, time spent: 0.0ms, 0.0% of total-time

simplify17.0ms (0.1%)

Algorithm
egg-herbie
Rules
17×*-commutative
+-commutative
sub-neg
1-exp
neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076609
1100609
2109609
3115609
4119609
5120609
Stop Event
fuel
saturated
Calls
Call 1
Inputs
(/.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 (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 5931188266773141/26959946667150639794667015087019630673637144422540572481103610249216 binary64)) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 2599999999999999900063346088055835535081472 binary64)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.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 29000000000000000595918337071783218478916243440075762942120183207997077077456276478975836184069590618307952989685649814671615453556034106083957323896689994863646353653760 binary64)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 9199999999999999726711750728200293463172566946305203158211719480040680392725389651200471131720457134019271356489812089825758758145843549042018088548378551941789567156224 binary64)) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
Outputs
(/.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 (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 5931188266773141/26959946667150639794667015087019630673637144422540572481103610249216 binary64)) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 5931188266773141/26959946667150639794667015087019630673637144422540572481103610249216 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 2599999999999999900063346088055835535081472 binary64)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.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 2599999999999999900063346088055835535081472 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.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 29000000000000000595918337071783218478916243440075762942120183207997077077456276478975836184069590618307952989685649814671615453556034106083957323896689994863646353653760 binary64)) (*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 29000000000000000595918337071783218478916243440075762942120183207997077077456276478975836184069590618307952989685649814671615453556034106083957323896689994863646353653760 binary64)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 9199999999999999726711750728200293463172566946305203158211719480040680392725389651200471131720457134019271356489812089825758758145843549042018088548378551941789567156224 binary64)) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 (/.f64 k (*.f64 (PI.f64) n)) k)) #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 9199999999999999726711750728200293463172566946305203158211719480040680392725389651200471131720457134019271356489812089825758758145843549042018088548378551941789567156224 binary64)) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
Compiler

Compiled 181 to 133 computations (26.5% saved)

soundness2.2s (10.3%)

Rules
1096×log1p-expm1-u
724×times-frac
693×fma-define
646×associate-*r*
644×times-frac
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
011338589975881
124698589974032
274188589974032
045517552
198516254
2312814844
026226
1427222
24798222
039438
196380
2211380
3410364
4686352
51171352
61433352
71698352
82017352
92060352
102088352
112099352
122101352
089729182
1211027744
2667626617
043453
1762424
037486
1622486
040365
1709365
27245365
Stop Event
node limit
node limit
node limit
node limit
saturated
node limit
node limit
node limit
Compiler

Compiled 1604 to 986 computations (38.5% saved)

end0.0ms (0%)

preprocess102.0ms (0.5%)

Compiler

Compiled 366 to 224 computations (38.8% saved)

Profiling

Loading profile data...