Migdal et al, Equation (51)

Time bar (total: 16.2s)

analyze157.0ms (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 14 computations (26.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 99.0ms
ival-pow: 45.0ms (45.2% of total)
ival-mult: 19.0ms (19.1% of total)
ival-div: 16.0ms (16.1% of total)
ival-sqrt: 7.0ms (7% of total)
ival-sub: 6.0ms (6% of total)
ival-pi: 4.0ms (4% of total)
const: 1.0ms (1% of total)
backward-pass: 0.0ms (0% of total)

sample5.0s (30.9%)

Results
1.3s8256×0valid
2.1s3750×5exit
647.0ms1883×1invalid
52.0ms559×0invalid
45.0ms253×0unsamplable
Precisions
Click to see histograms. Total time spent on operations: 2.8s
ival-pow: 829.0ms (29.4% of total)
ival-mult: 630.0ms (22.3% of total)
ival-sqrt: 402.0ms (14.2% of total)
ival-div: 348.0ms (12.3% of total)
backward-pass: 250.0ms (8.9% of total)
ival-sub: 230.0ms (8.2% of total)
ival-pi: 93.0ms (3.3% of total)
const: 39.0ms (1.4% of total)
Bogosity

preprocess132.0ms (0.8%)

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

Useful iterations: 4 (0.0ms)

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

explain188.0ms (1.2%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
3208(1.975225480965208e+256 9.32270298121128e+103)1(2.6430574197517012e-8 1.148279486238876e+82)(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
00-0-(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
00-0-(PI.f64)
00-0-(*.f64 #s(literal 2 binary64) (PI.f64))
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
00-0-(-.f64 #s(literal 1 binary64) k)
00-0-#s(literal 2 binary64)
00-0-(sqrt.f64 k)
00-0-(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
00-0-#s(literal 1 binary64)
00-0-(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
00-0-n
00-0-k
Results
132.0ms512×0valid
Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 99.0ms
ival-sqrt: 53.0ms (53.6% of total)
ival-pow: 17.0ms (17.2% of total)
ival-mult: 12.0ms (12.1% of total)
ival-div: 9.0ms (9.1% of total)
ival-sub: 3.0ms (3% of total)
ival-pi: 2.0ms (2% of total)
const: 1.0ms (1% of total)
backward-pass: 0.0ms (0% of total)

eval1.0ms (0%)

Compiler

Compiled 59 to 23 computations (61% saved)

prune2.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(/.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))
99.2%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Compiler

Compiled 34 to 25 computations (26.5% saved)

localize146.0ms (0.9%)

Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 k #s(literal 2 binary64))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 (PI.f64) n)
cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
cost-diff0
(sqrt.f64 k)
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy100.0%
(PI.f64)
accuracy99.7%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
accuracy99.6%
(*.f64 (PI.f64) n)
accuracy99.4%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
accuracy99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy99.4%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
Rules
17×fma-define
14×sub-neg
13×*-commutative
11×sub-neg
10×fma-define
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
019185
137179
254179
377179
497167
5116167
6143167
7172167
8183167
9187167
018168
124168
241168
352168
465168
578156
697156
7116156
8124156
Stop Event
saturated
saturated
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(/.f64 k #s(literal 2 binary64))
k
(sqrt.f64 k)
Outputs
(/.f64 (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 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 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 -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))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 k #s(literal 2 binary64))
k
(sqrt.f64 k)
Call 2
Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(*.f64 (/.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 -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 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)
Results
74.0ms256×0valid
Compiler

Compiled 105 to 21 computations (80% saved)

Precisions
Click to see histograms. Total time spent on operations: 46.0ms
ival-pow: 16.0ms (35% of total)
ival-mult: 12.0ms (26.3% of total)
ival-div: 7.0ms (15.3% of total)
ival-sub: 6.0ms (13.1% of total)
ival-sqrt: 2.0ms (4.4% of total)
ival-pi: 1.0ms (2.2% of total)
const: 1.0ms (2.2% of total)
backward-pass: 0.0ms (0% of total)

series151.0ms (0.9%)

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

42 calls:

TimeVariablePointExpression
68.0ms
n
@-inf
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
35.0ms
n
@0
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
9.0ms
k
@inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
7.0ms
n
@inf
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
1.0ms
k
@0
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))

rewrite302.0ms (1.9%)

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

simplify241.0ms (1.5%)

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

Useful iterations: 2 (0.0ms)

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

eval93.0ms (0.6%)

Compiler

Compiled 9611 to 1559 computations (83.8% saved)

prune81.0ms (0.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New44614460
Fresh000
Picked112
Done000
Total44715462
Accuracy
100.0%
Counts
462 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
75.1%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
99.3%
(/.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))
77.9%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
98.9%
(/.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))))
98.9%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
99.3%
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
75.9%
(*.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)))
75.9%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (*.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
55.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
75.6%
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
44.2%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
44.3%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
44.2%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
43.9%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
88.0%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) k))
Compiler

Compiled 502 to 360 computations (28.3% saved)

localize649.0ms (4%)

Algorithm
egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 k)
cost-diff0
(*.f64 k #s(literal 1/2 binary64))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
cost-diff0
(/.f64 k #s(literal 2 binary64))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 (PI.f64) n)
cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
cost-diff0
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
cost-diff0
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
cost-diff0
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)
cost-diff0
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
cost-diff0
(*.f64 n (/.f64 (PI.f64) k))
cost-diff0
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
cost-diff0
(-.f64 #s(literal 1 binary64) k)
cost-diff0
(PI.f64)
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
cost-diff0
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
accuracy99.6%
(/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
accuracy99.2%
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
accuracy98.9%
(*.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)))
accuracy78.1%
(PI.f64)
accuracy99.7%
(*.f64 (PI.f64) n)
accuracy99.4%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
accuracy78.1%
(PI.f64)
accuracy77.7%
(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
accuracy99.8%
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)
accuracy99.7%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
accuracy88.2%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
accuracy78.1%
(PI.f64)
accuracy99.6%
(/.f64 (PI.f64) k)
accuracy99.4%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
accuracy88.1%
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
accuracy78.1%
(PI.f64)
accuracy99.7%
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
accuracy99.7%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
accuracy99.4%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
accuracy78.1%
(PI.f64)
Rules
24×fma-define
24×fma-define
15×sub-neg
14×sub-neg
12×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019171
133171
250171
368159
493159
5114159
6147159
7179159
8194159
9197159
015110
119110
221110
323110
424110
017171
127171
234171
336171
020191
126191
243191
354191
467191
580179
699179
7118179
8126179
019222
129222
247198
373198
496198
5124198
6156198
7183198
8189198
Stop Event
saturated
saturated
saturated
saturated
saturated
Calls
Call 1
Inputs
(*.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)))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 k #s(literal 1/2 binary64))
k
(/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
n
(sqrt.f64 k)
Outputs
(*.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 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(/.f64 (*.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))))) (sqrt.f64 k))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.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 #s(literal 1/2 binary64) k)))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
k
(/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))
(/.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
n
(sqrt.f64 k)
Call 2
Inputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(/.f64 k #s(literal 2 binary64))
k
(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
(pow.f64 k #s(literal 3/2 binary64))
#s(literal 3/2 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)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 k #s(literal 2 binary64))
k
(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
(pow.f64 k #s(literal 3/2 binary64))
#s(literal 3/2 binary64)
Call 3
Inputs
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(+.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
Outputs
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)
(/.f64 (pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (+.f64 #s(literal 1 binary64) k)) k)
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k)) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) k)) k)
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (+.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1 binary64) k))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(+.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
Call 4
Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (/.f64 (PI.f64) k))
n
(/.f64 (PI.f64) k)
(PI.f64)
k
Outputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
n
(/.f64 (PI.f64) k)
(PI.f64)
k
Call 5
Inputs
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
Outputs
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(pow.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
Results
147.0ms198×0valid
341.0ms58×0unsamplable
Compiler

Compiled 252 to 40 computations (84.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 414.0ms
ival-pow: 218.0ms (52.7% of total)
ival-mult: 168.0ms (40.6% of total)
ival-div: 9.0ms (2.2% of total)
ival-sqrt: 8.0ms (1.9% of total)
ival-sub: 5.0ms (1.2% of total)
ival-cbrt: 2.0ms (0.5% of total)
ival-pi: 1.0ms (0.2% of total)
ival-add: 1.0ms (0.2% of total)
const: 1.0ms (0.2% of total)
backward-pass: 0.0ms (0% of total)

series133.0ms (0.8%)

Counts
18 → 312
Calls
Call 1
Inputs
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))>
#<alt (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))>
#<alt (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))>
#<alt (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))>
#<alt (/.f64 (PI.f64) k)>
#<alt (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))>
#<alt (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)>
#<alt (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))>
#<alt (*.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)))>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))>
#<alt (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))>
#<alt (-.f64 #s(literal 1 binary64) k)>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (*.f64 n (/.f64 (PI.f64) k))>
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))>
#<alt (*.f64 k #s(literal 1/2 binary64))>
Outputs
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<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)))))>
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#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt #s(literal 1 binary64)>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))>
#<alt (*.f64 #s(literal -1 binary64) k)>
#<alt (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))>
#<alt (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))>
#<alt (*.f64 k (-.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) k)>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 k (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) k))))>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))>
#<alt (exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))>
#<alt (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))>
#<alt (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (*.f64 k (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (*.f64 k (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)))))) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))))))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))>
#<alt (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))))>
#<alt (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))))>
#<alt (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))))>
#<alt (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))))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
Calls

81 calls:

TimeVariablePointExpression
35.0ms
n
@-inf
(* (pow (* 2 (PI)) (- 1/2 (* k 1/2))) (/ (pow n (- 1/2 (* k 1/2))) (sqrt k)))
20.0ms
n
@0
(* (pow (* 2 (PI)) (- 1/2 (* k 1/2))) (/ (pow n (- 1/2 (* k 1/2))) (sqrt k)))
15.0ms
n
@inf
(* (pow (* 2 (PI)) (- 1/2 (* k 1/2))) (/ (pow n (- 1/2 (* k 1/2))) (sqrt k)))
4.0ms
n
@-inf
(/ (pow n (- 1/2 (* k 1/2))) (sqrt k))
3.0ms
k
@inf
(sqrt (* n (/ (PI) k)))

rewrite186.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
310×log1p-expm1-u
310×expm1-log1p-u
303×pow1
298×add-cube-cbrt
297×add-exp-log
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
041519
1713488
Stop Event
node limit
Counts
18 → 397
Calls
Call 1
Inputs
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(/.f64 (PI.f64) k)
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) k)
(cbrt.f64 (pow.f64 k #s(literal 3/2 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)))
(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 #s(literal 1 binary64) k)
(sqrt.f64 #s(literal 2 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 k #s(literal 1/2 binary64))
Outputs
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 n) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 n) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (neg.f64 k)))
(*.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(log.f64 (exp.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)) n))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal -1/2 binary64))))) #s(literal 1 binary64))
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
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(pow.f64 (pow.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))) #s(literal 2 binary64))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) #s(literal -1 binary64))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) #s(literal 2 binary64)) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k)) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) #s(literal 3 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k))) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (neg.f64 k))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) k))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (cbrt.f64 (-.f64 #s(literal 1 binary64) k)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 (-.f64 #s(literal 1 binary64) k)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 k k k))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (fma.f64 k k k)) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 k k k)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) k))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) k)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 k k k))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 k) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (neg.f64 k) (neg.f64 k)) (neg.f64 k))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 k) (neg.f64 k))) (-.f64 #s(literal 1 binary64) (neg.f64 k)))
(pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(log.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (-.f64 #s(literal 1 binary64) k))))
(cbrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (-.f64 #s(literal 1 binary64) k)))
(log1p.f64 (expm1.f64 (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (log1p.f64 (neg.f64 k)))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (cbrt.f64 #s(literal 2 binary64)) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(log.f64 (exp.f64 (sqrt.f64 #s(literal 2 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 #s(literal 2 binary64)))))
(cbrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 #s(literal 2 binary64))))
(log1p.f64 (expm1.f64 (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 1 binary64))
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (neg.f64 (*.f64 n (PI.f64))) (neg.f64 k))
(pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) k)) n))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k))))
(exp.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (pow.f64 n (+.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 n (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (PI.f64) (+.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64)))
(log.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)) n))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) k))) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (pow.f64 (exp.f64 k) #s(literal 1/2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 1/2 binary64) k))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) k)))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 1/2 binary64) k)))
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) k)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) k)) #s(literal 1 binary64)))

simplify437.0ms (2.7%)

Algorithm
egg-herbie
Rules
357×fma-define
351×times-frac
313×*-commutative
290×exp-prod
248×associate-/r*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0115131348
1259029700
2646928056
Stop Event
node limit
Counts
709 → 660
Calls
Call 1
Inputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
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(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) k))) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (pow.f64 (exp.f64 k) #s(literal 1/2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 1/2 binary64) k))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) k)))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 1/2 binary64) k)))
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) k)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) k)) #s(literal 1 binary64)))
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 k (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 k (fma.f64 #s(literal 1/8 binary64) (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 k (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 k (fma.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 k (fma.f64 k (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)))) (*.f64 #s(literal -1/48 binary64) (*.f64 k (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.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 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
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(pow.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(sqrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) k)) n))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64)))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64))))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3/2 binary64))))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(*.f64 n (/.f64 (PI.f64) k))
(expm1.f64 (log1p.f64 (*.f64 n (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (*.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64)))
(*.f64 n (/.f64 (PI.f64) k))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.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)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 (pow.f64 n (+.f64 #s(literal 1 binary64) k)) (pow.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)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 n (+.f64 #s(literal 1 binary64) k)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.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)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))) (sqrt.f64 (pow.f64 (*.f64 n (*.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)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.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)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(*.f64 (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (PI.f64)) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) k)))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) k)))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) k)) (pow.f64 (PI.f64) (+.f64 #s(literal 1 binary64) k)))
(sqrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(log.f64 (exp.f64 (pow.f64 (*.f64 n (*.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)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (*.f64 n (*.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)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 n (*.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)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(exp.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(exp.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) k) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (+.f64 #s(literal 1 binary64) k)))
(pow.f64 (exp.f64 (+.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) k))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)) n))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(log1p.f64 (expm1.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(exp.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) k))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(pow.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) k)) #s(literal 3 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(pow.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(pow.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fabs.f64 (*.f64 #s(literal 1/2 binary64) k))
(log.f64 (pow.f64 (exp.f64 k) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 #s(literal 1/2 binary64) k)
(cbrt.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 3 binary64)))
(*.f64 #s(literal 1/2 binary64) k)
(expm1.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) k)))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 #s(literal 1/2 binary64) k)
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) k)))
(*.f64 #s(literal 1/2 binary64) k)
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) k)) #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) k)

eval298.0ms (1.8%)

Compiler

Compiled 19371 to 3236 computations (83.3% saved)

prune874.0ms (5.4%)

Pruning

20 alts after pruning (18 fresh and 2 done)

PrunedKeptTotal
New90613919
Fresh459
Picked415
Done011
Total91420934
Accuracy
100.0%
Counts
934 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
75.1%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
99.3%
(/.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))
77.9%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
98.9%
(/.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))))
98.9%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
55.7%
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
59.4%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))))
43.6%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (+.f64 (sqrt.f64 (*.f64 n k)) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 n) (sqrt.f64 (*.f64 n (pow.f64 k #s(literal 3 binary64))))))) k))
73.0%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (expm1.f64 (log1p.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k)))))
75.9%
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
44.2%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
55.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
44.2%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
44.2%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))))
44.3%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
75.9%
(*.f64 (exp.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
88.0%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
44.4%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
44.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
44.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
Compiler

Compiled 642 to 474 computations (26.2% saved)

localize519.0ms (3.2%)

Algorithm
egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 k)
cost-diff0
(*.f64 k #s(literal -1/2 binary64))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 #s(literal 2 binary64) (PI.f64))
cost-diff0
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
cost-diff128
(*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
cost-diff192
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)))
cost-diff192
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
cost-diff0
(/.f64 n (/.f64 k (PI.f64)))
cost-diff0
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
cost-diff0
(/.f64 (PI.f64) k)
cost-diff0
(*.f64 n (/.f64 (PI.f64) k))
cost-diff0
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
cost-diff0
(pow.f64 k #s(literal -1/2 binary64))
cost-diff0
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
cost-diff0
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
accuracy99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
accuracy99.4%
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
accuracy99.2%
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
accuracy77.7%
(PI.f64)
accuracy99.7%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
accuracy99.6%
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
accuracy99.1%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)))
accuracy77.7%
(PI.f64)
accuracy99.7%
(/.f64 n (/.f64 k (PI.f64)))
accuracy99.4%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
accuracy88.1%
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
accuracy77.7%
(PI.f64)
accuracy99.7%
(*.f64 n (/.f64 (PI.f64) k))
accuracy99.6%
(/.f64 (PI.f64) k)
accuracy88.1%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
accuracy77.7%
(PI.f64)
accuracy99.6%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
accuracy99.6%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
accuracy99.1%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
accuracy77.7%
(PI.f64)
Rules
13×*-commutative
12×associate-*l*
10×associate-*r*
*-commutative
*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
020231
128231
238231
341231
014103
120103
235103
349103
461103
571103
015110
118110
221110
325110
426110
018112
130112
237112
339112
020228
126204
233204
334204
Stop Event
saturated
saturated
saturated
saturated
saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 k)
(pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
n
Outputs
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 (*.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))))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 k)
(pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
n
Call 2
Inputs
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
Outputs
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
n
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
Call 3
Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 n (/.f64 k (PI.f64)))
n
(/.f64 k (PI.f64))
k
(PI.f64)
Outputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
n
(/.f64 k (PI.f64))
k
(PI.f64)
Call 4
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
#s(literal 2 binary64)
(*.f64 n (/.f64 (PI.f64) k))
n
(/.f64 (PI.f64) k)
(PI.f64)
k
Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) k) (*.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))
(*.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
#s(literal 2 binary64)
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
n
(/.f64 (PI.f64) k)
(PI.f64)
k
Call 5
Inputs
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
Outputs
(/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (*.f64 (*.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 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.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 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 k #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
Results
102.0ms197×0valid
34.0ms58×0unsamplable
2.0ms5exit
Compiler

Compiled 234 to 37 computations (84.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 90.0ms
ival-pow: 44.0ms (48.7% of total)
ival-mult: 24.0ms (26.6% of total)
ival-sqrt: 10.0ms (11.1% of total)
ival-div: 9.0ms (10% of total)
ival-pi: 1.0ms (1.1% of total)
ival-add: 1.0ms (1.1% of total)
const: 1.0ms (1.1% of total)
backward-pass: 0.0ms (0% of total)

series63.0ms (0.4%)

Counts
17 → 312
Calls
Call 1
Inputs
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))>
#<alt (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))>
#<alt (sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))>
#<alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))>
#<alt (/.f64 n (/.f64 k (PI.f64)))>
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)))>
#<alt (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))) (pow.f64 k #s(literal -1/2 binary64)))>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))>
#<alt (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))>
#<alt (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))>
#<alt (/.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))>
#<alt (pow.f64 k #s(literal -1/2 binary64))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))>
#<alt (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))>
#<alt (*.f64 k #s(literal -1/2 binary64))>
Outputs
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
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#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
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#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))))>
#<alt (*.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.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 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
Calls

78 calls:

TimeVariablePointExpression
7.0ms
k
@0
(* (/ (pow (* 2 (PI)) (+ 1/2 (* k -1/2))) (sqrt k)) (pow n (+ 1/2 (* k -1/2))))
2.0ms
k
@0
(/ (* (pow k -1/2) (sqrt (* 2 (* (PI) n)))) (pow (* 2 (* (PI) n)) (* k 1/2)))
2.0ms
n
@0
(* (/ (pow (* 2 (PI)) (+ 1/2 (* k -1/2))) (sqrt k)) (pow n (+ 1/2 (* k -1/2))))
1.0ms
n
@-inf
(* (/ (pow (* 2 (PI)) (+ 1/2 (* k -1/2))) (sqrt k)) (pow n (+ 1/2 (* k -1/2))))
1.0ms
n
@-inf
(/ (* (pow k -1/2) (sqrt (* 2 (* (PI) n)))) (pow (* 2 (* (PI) n)) (* k 1/2)))

rewrite144.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
314×associate-*r*
279×log1p-expm1-u
279×expm1-log1p-u
277×pow1
272×add-exp-log
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
042540
1729456
Stop Event
node limit
Counts
17 → 433
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(/.f64 n (/.f64 k (PI.f64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (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 k #s(literal -1/2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
(*.f64 k #s(literal -1/2 binary64))
Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
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(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal -1 binary64))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(sqrt.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(exp.f64 (log.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (cbrt.f64 (/.f64 #s(literal 1 binary64) k)) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (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 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cbrt.f64 k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (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 (*.f64 #s(literal -1/2 binary64) (log.f64 k)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) #s(literal 1 binary64)))
(exp.f64 (neg.f64 (log.f64 (sqrt.f64 k))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) #s(literal 1 binary64))
(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))
(/.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k (PI.f64)))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) k)) n) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 1 binary64)))
#s(literal 1/2 binary64)
(-.f64 (exp.f64 (log1p.f64 (*.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal -1/8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 2 binary64))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (pow.f64 (exp.f64 k) #s(literal -1/2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 k #s(literal -1/2 binary64)))))
(cbrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal -1/8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 k #s(literal -1/2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 k #s(literal -1/2 binary64))))
(exp.f64 (log.f64 (*.f64 k #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)))

simplify445.0ms (2.7%)

Algorithm
egg-herbie
Rules
980×fma-define
737×times-frac
312×*-commutative
244×exp-prod
242×associate-*r/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0103431390
1242330602
2525330014
Stop Event
node limit
Counts
745 → 607
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))))
(+.f64 #s(literal 1 binary64) (*.f64 k (+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))) (*.f64 k (+.f64 (*.f64 #s(literal 1/48 binary64) (*.f64 k (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 k (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))
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(log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #s(literal 1 binary64))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (cbrt.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(*.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (cbrt.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal -1 binary64))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) (neg.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k)))
(sqrt.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(exp.f64 (log.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (cbrt.f64 (/.f64 #s(literal 1 binary64) k)) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (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 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cbrt.f64 k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (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 (*.f64 #s(literal -1/2 binary64) (log.f64 k)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) #s(literal 1 binary64)))
(exp.f64 (neg.f64 (log.f64 (sqrt.f64 k))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) #s(literal 1 binary64))
(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))
(/.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k (PI.f64)))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) k)) n) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 1 binary64)))
#s(literal 1/2 binary64)
(-.f64 (exp.f64 (log1p.f64 (*.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal -1/8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 2 binary64))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (pow.f64 (exp.f64 k) #s(literal -1/2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 k #s(literal -1/2 binary64)))))
(cbrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal -1/8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 k #s(literal -1/2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 k #s(literal -1/2 binary64))))
(exp.f64 (log.f64 (*.f64 k #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)))
Outputs
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
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(cbrt.f64 (pow.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) k) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) k) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) k) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(+.f64 #s(literal -1 binary64) (fma.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 (cbrt.f64 (/.f64 #s(literal 1 binary64) k)) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(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)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cbrt.f64 k) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(literal 1 binary64)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.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))))
(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)))))
(pow.f64 k #s(literal -1/2 binary64))
(cbrt.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
(expm1.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64))))
(log1p.f64 (expm1.f64 (pow.f64 k #s(literal -1/2 binary64))))
(pow.f64 k #s(literal -1/2 binary64))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)))
(pow.f64 k #s(literal -1/2 binary64))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)) #s(literal 1 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
(exp.f64 (neg.f64 (log.f64 (sqrt.f64 k))))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
(+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) #s(literal 1 binary64)))
(/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(/.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 3 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(pow.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 4 binary64)))
(sqrt.f64 (pow.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) k)) n) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))) #s(literal 3 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(expm1.f64 (log1p.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
(+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
#s(literal 1/2 binary64)
(-.f64 (exp.f64 (log1p.f64 (*.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (*.f64 k #s(literal -1/2 binary64))))
(+.f64 #s(literal -1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1 binary64)))
(pow.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 k #s(literal -1/2 binary64))
(pow.f64 (cbrt.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64))
(*.f64 k #s(literal -1/2 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal -1/8 binary64)) #s(literal 1/3 binary64))
(cbrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal -1/8 binary64)))
(pow.f64 (sqrt.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 2 binary64))
(*.f64 k #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (pow.f64 k #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 k #s(literal 2 binary64))))
(log.f64 (pow.f64 (exp.f64 k) #s(literal -1/2 binary64)))
(*.f64 k #s(literal -1/2 binary64))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 k #s(literal -1/2 binary64))
(cbrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal -1/8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 k #s(literal -1/2 binary64))))
(+.f64 #s(literal -1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (*.f64 k #s(literal -1/2 binary64))))
(*.f64 k #s(literal -1/2 binary64))
(exp.f64 (log.f64 (*.f64 k #s(literal -1/2 binary64))))
(*.f64 k #s(literal -1/2 binary64))
(exp.f64 (*.f64 (log.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 k #s(literal -1/2 binary64))

eval125.0ms (0.8%)

Compiler

Compiled 19478 to 3253 computations (83.3% saved)

prune201.0ms (1.2%)

Pruning

24 alts after pruning (21 fresh and 3 done)

PrunedKeptTotal
New90512917
Fresh4913
Picked325
Done112
Total91324937
Accuracy
100.0%
Counts
937 → 24
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(/.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))
78.3%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
59.4%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))))
43.6%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (+.f64 (sqrt.f64 (*.f64 n k)) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 n) (sqrt.f64 (*.f64 n (pow.f64 k #s(literal 3 binary64))))))) k))
73.0%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (expm1.f64 (log1p.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k)))))
55.7%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
75.9%
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
55.7%
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
99.0%
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
44.2%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
56.0%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
44.4%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
44.4%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
55.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
44.3%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
75.9%
(*.f64 (exp.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
88.0%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
44.3%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
42.6%
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) #s(literal 1 binary64))))
44.4%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
44.4%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
44.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
44.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
44.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
Compiler

Compiled 674 to 518 computations (23.1% saved)

localize655.0ms (4%)

Algorithm
egg-herbie
Localize:

Found 40 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 n)
cost-diff0
(pow.f64 k #s(literal -1/2 binary64))
cost-diff0
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n))
cost-diff0
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
cost-diff0
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff128
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
cost-diff0
(*.f64 (/.f64 n k) (PI.f64))
cost-diff0
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
cost-diff0
(/.f64 k (PI.f64))
cost-diff0
(/.f64 n (/.f64 k (PI.f64)))
cost-diff0
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
cost-diff0
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
cost-diff0
(PI.f64)
cost-diff0
(/.f64 (PI.f64) k)
cost-diff0
(sqrt.f64 (/.f64 (PI.f64) k))
cost-diff0
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))
accuracy100.0%
(PI.f64)
accuracy99.5%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n))
accuracy99.3%
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
accuracy98.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
accuracy99.6%
(*.f64 n (PI.f64))
accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
accuracy99.3%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
accuracy77.9%
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
accuracy100.0%
(PI.f64)
accuracy99.6%
(*.f64 (/.f64 n k) (PI.f64))
accuracy99.3%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
accuracy78.5%
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
accuracy100.0%
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
accuracy99.7%
(/.f64 k (PI.f64))
accuracy99.7%
(/.f64 n (/.f64 k (PI.f64)))
accuracy78.6%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
accuracy99.9%
(sqrt.f64 (/.f64 (PI.f64) k))
accuracy99.7%
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
accuracy99.5%
(/.f64 (PI.f64) k)
accuracy99.3%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))
Rules
11×*-commutative
10×associate-*r*
associate-*l*
associate-*l/
*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
020180
126168
236168
338168
014103
119103
230103
352103
465103
573103
015111
119111
223111
324111
017148
128142
233142
340142
440142
017117
122117
229117
331117
Stop Event
saturated
saturated
saturated
saturated
saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n))
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 n)
n
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
Outputs
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n))
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(sqrt.f64 n)
n
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
Call 2
Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(/.f64 k (*.f64 n (PI.f64)))
k
(*.f64 n (PI.f64))
n
(PI.f64)
Outputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(/.f64 k (*.f64 n (PI.f64)))
k
(*.f64 n (PI.f64))
n
(PI.f64)
Call 3
Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(/.f64 n k)
n
k
(PI.f64)
Outputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (/.f64 n k) (PI.f64))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 n k)
n
k
(PI.f64)
Call 4
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
#s(literal 2 binary64)
(/.f64 n (/.f64 k (PI.f64)))
n
(/.f64 k (PI.f64))
k
(PI.f64)
Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 n k) (*.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k)))
#s(literal 2 binary64)
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
n
(/.f64 k (PI.f64))
k
(PI.f64)
Call 5
Inputs
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(PI.f64)
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
n
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
Outputs
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(PI.f64)
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
n
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
Results
427.0ms256×0valid
Compiler

Compiled 185 to 35 computations (81.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 333.0ms
ival-pow: 224.0ms (67.3% of total)
ival-mult: 82.0ms (24.6% of total)
ival-sqrt: 13.0ms (3.9% of total)
ival-div: 11.0ms (3.3% of total)
ival-pi: 1.0ms (0.3% of total)
ival-add: 1.0ms (0.3% of total)
const: 1.0ms (0.3% of total)
backward-pass: 0.0ms (0% of total)

series43.0ms (0.3%)

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

81 calls:

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

rewrite195.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
309×associate-*r*
272×log1p-expm1-u
272×expm1-log1p-u
269×pow1
269×add-cube-cbrt
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
040405
1682395
Stop Event
node limit
Counts
17 → 479
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(sqrt.f64 (/.f64 (PI.f64) k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(/.f64 k (PI.f64))
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (/.f64 n k) (PI.f64))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(*.f64 n (PI.f64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n))
(sqrt.f64 n)
Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #s(literal 1 binary64))
(pow.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(sqrt.f64 (*.f64 (pow.f64 n (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (PI.f64) k)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))) (cbrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (cbrt.f64 (/.f64 (PI.f64) k)) (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (/.f64 (PI.f64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (PI.f64) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (/.f64 (PI.f64) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) k)))))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 n) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 #s(literal 2 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))))
(*.f64 (cbrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (cbrt.f64 (/.f64 n k)) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))) (cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 n k))))
(*.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))))
(*.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))) (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(*.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 (PI.f64) (/.f64 k n)))))
(*.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 n k))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 n k))) (*.f64 (sqrt.f64 (sqrt.f64 (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (*.f64 (pow.f64 k #s(literal -1/4 binary64)) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (cbrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 (cbrt.f64 #s(literal 2 binary64)) (cbrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(*.f64 (/.f64 (cbrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (cbrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 n k)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 n))
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(cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(cbrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 n k)))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 n) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 n)) (sqrt.f64 (neg.f64 k)))
(pow.f64 (/.f64 n k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 n k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 n k))) #s(literal 2 binary64))
(sqrt.f64 (/.f64 n k))
(fabs.f64 (sqrt.f64 (/.f64 n k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 n k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 n k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 n k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 n k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 n k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 n k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 n))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 n))
(*.f64 (cbrt.f64 (sqrt.f64 n)) (cbrt.f64 n))
(*.f64 (cbrt.f64 n) (cbrt.f64 (sqrt.f64 n)))
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 n #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 n))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 n) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 n)))
(pow.f64 n #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 n) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 n)) #s(literal 3 binary64))
(pow.f64 (pow.f64 n #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 n #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 n))
(log.f64 (exp.f64 (sqrt.f64 n)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 n))))
(cbrt.f64 (pow.f64 n #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 n)))
(log1p.f64 (expm1.f64 (sqrt.f64 n)))
(exp.f64 (log.f64 (sqrt.f64 n)))
(exp.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 n)) #s(literal 1 binary64)))

simplify297.0ms (1.8%)

Algorithm
egg-herbie
Rules
550×fma-define
450×associate-*r*
414×associate-*l*
356×exp-prod
294×*-commutative
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
083224578
1156522852
2498622770
Stop Event
node limit
Counts
739 → 524
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.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 n) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 n) (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 n) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 n) (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 n) #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 n) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (exp.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
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(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
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(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
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(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(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))))
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(*.f64 (pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k n))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k n))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k n)))))
(pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1 binary64))
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))
(fabs.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) #s(literal 1 binary64))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 n) (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (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 (PI.f64) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 #s(literal 2 binary64)) (*.f64 (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (cbrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))
(fabs.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 3/2 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(cbrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 n k)))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 n) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 n)) (sqrt.f64 (neg.f64 k)))
(pow.f64 (/.f64 n k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 n k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 n k))) #s(literal 2 binary64))
(sqrt.f64 (/.f64 n k))
(fabs.f64 (sqrt.f64 (/.f64 n k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 n k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 n k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 n k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 n k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 n k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 n k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 n))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 n))
(*.f64 (cbrt.f64 (sqrt.f64 n)) (cbrt.f64 n))
(*.f64 (cbrt.f64 n) (cbrt.f64 (sqrt.f64 n)))
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 n #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 n))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 n) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 n)))
(pow.f64 n #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 n) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 n)) #s(literal 3 binary64))
(pow.f64 (pow.f64 n #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 n #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 n))
(log.f64 (exp.f64 (sqrt.f64 n)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 n))))
(cbrt.f64 (pow.f64 n #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 n)))
(log1p.f64 (expm1.f64 (sqrt.f64 n)))
(exp.f64 (log.f64 (sqrt.f64 n)))
(exp.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 n)) #s(literal 1 binary64)))
Outputs
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)))
(/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 n) (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 (PI.f64) n))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 n))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64))))) k)
(/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 n)) #s(literal -1/2 binary64)))) k)
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 n)) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 (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 n) (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 n) #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 n)) (sqrt.f64 (*.f64 (*.f64 k n) (PI.f64)))) (*.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 n) #s(literal 2 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 k 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 n) (sqrt.f64 (*.f64 k (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 n) #s(literal 2 binary64))) #s(literal 1/8 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 (PI.f64) n))))) k)
(/.f64 (fma.f64 k (fma.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 n) #s(literal 2 binary64))) #s(literal 1/8 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 n)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 k (*.f64 (PI.f64) n)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 k (*.f64 (PI.f64) n))))) k)
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(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))) #s(literal 3/2 binary64)))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(fabs.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))) #s(literal 3/2 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (/.f64 n k) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (/.f64 n k) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 3/2 binary64)))))
(cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 3/2 binary64)))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 3/2 binary64)))))
(cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (PI.f64) n) k) #s(literal 3/2 binary64)))))
(cbrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 3/2 binary64)))))
(cbrt.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 3/2 binary64)))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 n k)))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 n) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 n)) (sqrt.f64 (neg.f64 k)))
(pow.f64 (/.f64 n k) #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 n k))
(pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 n k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 n k))) #s(literal 3 binary64))
(sqrt.f64 (/.f64 n k))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 n k))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 n k))) #s(literal 2 binary64))
(sqrt.f64 (/.f64 n k))
(sqrt.f64 (/.f64 n k))
(fabs.f64 (sqrt.f64 (/.f64 n k)))
(sqrt.f64 (/.f64 n k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 n k))))
(sqrt.f64 (/.f64 n k))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 n k)))))
(sqrt.f64 (/.f64 n k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal 3 binary64)))
(sqrt.f64 (/.f64 n k))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 n k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 n k))))
(sqrt.f64 (/.f64 n k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 n k))))
(sqrt.f64 (/.f64 n k))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 n k))) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 n k))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 n))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (sqrt.f64 n)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 n))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(*.f64 (cbrt.f64 (sqrt.f64 n)) (cbrt.f64 n))
(*.f64 (cbrt.f64 n) (cbrt.f64 (sqrt.f64 n)))
(*.f64 (cbrt.f64 (sqrt.f64 n)) (cbrt.f64 n))
(*.f64 (pow.f64 n #s(literal 1/4 binary64)) (pow.f64 n #s(literal 1/4 binary64)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 n))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 n) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 n)))
(*.f64 (fabs.f64 (cbrt.f64 n)) (sqrt.f64 (cbrt.f64 n)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 n)))
(*.f64 (fabs.f64 (cbrt.f64 n)) (sqrt.f64 (cbrt.f64 n)))
(pow.f64 n #s(literal 1/2 binary64))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(pow.f64 (sqrt.f64 n) #s(literal 1 binary64))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(pow.f64 (cbrt.f64 (sqrt.f64 n)) #s(literal 3 binary64))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(pow.f64 (pow.f64 n #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(cbrt.f64 (pow.f64 n #s(literal 3/2 binary64)))
(pow.f64 (pow.f64 n #s(literal 1/4 binary64)) #s(literal 2 binary64))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(fabs.f64 (sqrt.f64 n))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(log.f64 (exp.f64 (sqrt.f64 n)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 n))))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(cbrt.f64 (pow.f64 n #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 n)))
(log1p.f64 (expm1.f64 (sqrt.f64 n)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(exp.f64 (log.f64 (sqrt.f64 n)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(exp.f64 (*.f64 (log.f64 n) #s(literal 1/2 binary64)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 n)) #s(literal 1 binary64)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 n)))
(sqrt.f64 n)

eval144.0ms (0.9%)

Compiler

Compiled 12063 to 2733 computations (77.3% saved)

prune291.0ms (1.8%)

Pruning

32 alts after pruning (27 fresh and 5 done)

PrunedKeptTotal
New80016816
Fresh51116
Picked325
Done033
Total80832840
Accuracy
100.0%
Counts
840 → 32
Alt Table
Click to see full alt table
StatusAccuracyProgram
34.6%
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
44.1%
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
99.3%
(/.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))
78.3%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
56.0%
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 k (PI.f64))))
44.5%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
43.6%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (+.f64 (sqrt.f64 (*.f64 n k)) (*.f64 #s(literal -1/2 binary64) (*.f64 (log.f64 n) (sqrt.f64 (*.f64 n (pow.f64 k #s(literal 3 binary64))))))) k))
73.0%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (expm1.f64 (log1p.f64 (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (sqrt.f64 k)))))
55.7%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))))
75.9%
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
44.2%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
56.0%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
44.1%
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
99.1%
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
44.4%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)))
55.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
44.3%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
95.3%
(*.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
88.0%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
44.3%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
42.6%
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) #s(literal 1 binary64))))
44.4%
(sqrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
44.4%
(sqrt.f64 (*.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
44.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
44.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
44.3%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 k (/.f64 #s(literal 1 binary64) (PI.f64))))))
42.6%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
44.3%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
44.4%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
41.5%
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n)))) #s(literal 1/2 binary64)))
36.9%
(cbrt.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)) #s(literal 3/2 binary64)))
36.9%
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k))) #s(literal 3/2 binary64)))
Compiler

Compiled 1178 to 567 computations (51.9% saved)

regimes66.0ms (0.4%)

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

4 calls:

16.0ms
n
15.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
15.0ms
k
15.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.3%1k
99.3%1n
99.3%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.3%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes25.0ms (0.2%)

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

2 calls:

10.0ms
k
10.0ms
n
Results
AccuracySegmentsBranch
99.1%1k
99.1%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes26.0ms (0.2%)

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

2 calls:

9.0ms
k
9.0ms
n
Results
AccuracySegmentsBranch
99.6%2k
90.4%2n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes21.0ms (0.1%)

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

2 calls:

9.0ms
n
9.0ms
k
Results
AccuracySegmentsBranch
63.6%3n
66.8%2k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

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

1 calls:

7.0ms
k
Results
AccuracySegmentsBranch
66.8%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes15.0ms (0.1%)

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

2 calls:

7.0ms
k
7.0ms
n
Results
AccuracySegmentsBranch
56.0%1n
56.0%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes209.0ms (1.3%)

Accuracy

Total -0.3b remaining (-0.9%)

Threshold costs -0.3b (-0.9%)

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

2 calls:

203.0ms
k
4.0ms
n
Results
AccuracySegmentsBranch
44.4%1k
44.4%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch19.0ms (0.1%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
17.0ms
3.6699019340096123e-16
4.583251517773482e-14
Results
13.0ms112×0valid
Compiler

Compiled 212 to 171 computations (19.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-pow: 3.0ms (31.6% of total)
ival-div: 2.0ms (21.1% of total)
ival-mult: 2.0ms (21.1% of total)
ival-sub: 1.0ms (10.5% of total)
ival-sqrt: 1.0ms (10.5% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch90.0ms (0.6%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
88.0ms
4.73864622873089e+68
1.6247638536484783e+70
Results
84.0ms112×0valid
Compiler

Compiled 205 to 171 computations (16.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-pow: 5.0ms (45.4% of total)
ival-div: 2.0ms (18.1% of total)
ival-mult: 2.0ms (18.1% of total)
ival-sub: 1.0ms (9.1% of total)
ival-sqrt: 1.0ms (9.1% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch67.0ms (0.4%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
66.0ms
4.73864622873089e+68
1.6247638536484783e+70
Results
61.0ms112×0valid
Compiler

Compiled 205 to 171 computations (16.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-pow: 5.0ms (45% of total)
ival-div: 2.0ms (18% of total)
ival-mult: 2.0ms (18% of total)
ival-sub: 1.0ms (9% of total)
ival-sqrt: 1.0ms (9% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify87.0ms (0.5%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
063435
188435
297435
3103435
4107435
5108435
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(if (<=.f64 k #s(literal 8315787937497185/20282409603651670423947251286016 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 500000000000000036265718190764617563079187204823260977759105077739520 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) #s(literal 1 binary64)))))
(if (<=.f64 k #s(literal 480000000000000015658895202310422131076681877251465743414501847334912 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))
Outputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (pow.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) k))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(if (<=.f64 k #s(literal 8315787937497185/20282409603651670423947251286016 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 8315787937497185/20282409603651670423947251286016 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 500000000000000036265718190764617563079187204823260977759105077739520 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) #s(literal 1 binary64)))))
(if (<=.f64 k #s(literal 500000000000000036265718190764617563079187204823260977759105077739520 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(if (<=.f64 k #s(literal 480000000000000015658895202310422131076681877251465743414501847334912 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 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))))))
(if (<=.f64 k #s(literal 480000000000000015658895202310422131076681877251465743414501847334912 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))

soundness3.2s (19.6%)

Rules
1096×log1p-expm1-u
980×fma-define
737×times-frac
724×fma-define
550×fma-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026274
1427270
24798270
039438
196380
2211380
3410364
4686352
51171352
61433352
71698352
82017352
92060352
102088352
112099352
122101352
0103431390
1242330602
2525330014
040405
1682395
0115131348
1259029700
2646928056
059819230
1121217176
2421516542
083224578
1156522852
2498622770
042540
1729456
041519
1713488
Stop Event
fuel
node limit
node limit
node limit
node limit
node limit
node limit
node limit
saturated
node limit
Compiler

Compiled 2381 to 651 computations (72.7% saved)

preprocess197.0ms (1.2%)

Compiler

Compiled 276 to 132 computations (52.2% saved)

end0.0ms (0%)

Profiling

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