Migdal et al, Equation (51)

Time bar (total: 16.8s)

analyze304.0ms (1.8%)

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

Compiled 19 to 16 computations (15.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 99.0ms
ival-pow: 47.0ms (47.3% of total)
ival-mult: 22.0ms (22.1% of total)
ival-div: 12.0ms (12.1% of total)
ival-sqrt: 8.0ms (8% of total)
ival-sub: 4.0ms (4% of total)
ival-pi: 3.0ms (3% of total)
const: 2.0ms (2% of total)

sample8.2s (49.1%)

Results
1.1s6185×0valid
4.4s3814×5exit
446.0ms2071×0infinite
544.0ms1894×1invalid
53.0ms580×0invalid
29.0ms204×0unsamplable
Precisions
Click to see histograms. Total time spent on operations: 5.1s
ival-pow: 1.6s (32.2% of total)
ival-mult: 911.0ms (17.8% of total)
ival-div: 768.0ms (15% of total)
backward-pass: 530.0ms (10.3% of total)
ival-sqrt: 503.0ms (9.8% of total)
ival-pi: 339.0ms (6.6% of total)
ival-sub: 328.0ms (6.4% of total)
const: 96.0ms (1.9% of total)
Bogosity

preprocess128.0ms (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 (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 (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 (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 (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 (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 (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 (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))

explain241.0ms (1.4%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2220(2.7362940939789425e-298 6.587171531761774e-233)1(0.00012268705736255976 3.596619833723709e+63)(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
122.0ms386×256valid
43.0ms126×256infinite
Compiler

Compiled 132 to 93 computations (29.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 117.0ms
ival-pow: 40.0ms (34.1% of total)
ival-mult: 31.0ms (26.4% of total)
ival-div: 22.0ms (18.7% of total)
ival-sub: 11.0ms (9.4% of total)
ival-sqrt: 6.0ms (5.1% of total)
ival-pi: 4.0ms (3.4% of total)
const: 4.0ms (3.4% of total)

eval1.0ms (0%)

Compiler

Compiled 15 to 12 computations (20% saved)

prune1.0ms (0%)

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

Compiled 33 to 27 computations (18.2% saved)

localize187.0ms (1.1%)

Localize:

Found 7 expressions with local error:

NewAccuracyProgram
99.8%
(/.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))
99.8%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
99.6%
(*.f64 (PI.f64) n)
99.8%
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
Results
110.0ms193×256valid
35.0ms63×256infinite
Compiler

Compiled 100 to 61 computations (39% saved)

Precisions
Click to see histograms. Total time spent on operations: 117.0ms
ival-pow: 46.0ms (39.2% of total)
ival-mult: 29.0ms (24.7% of total)
ival-div: 13.0ms (11.1% of total)
composed: 11.0ms (9.4% of total)
ival-sub: 5.0ms (4.3% of total)
ival-add: 4.0ms (3.4% of total)
ival-sqrt: 4.0ms (3.4% of total)
const: 3.0ms (2.6% of total)
ival-pi: 1.0ms (0.9% of total)

series207.0ms (1.2%)

Counts
7 → 132
Calls
Call 1
Inputs
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))>
#<alt (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))>
#<alt (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))>
#<alt (*.f64 (PI.f64) n)>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))>
#<alt (/.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))>
Outputs
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
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#<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)))))>
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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)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k)))))>
Calls

33 calls:

TimeVariablePointExpression
149.0ms
n
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
26.0ms
n
@-inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
9.0ms
n
@inf
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
2.0ms
k
@0
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms
k
@inf
(pow (* 2 (* (PI) n)) (+ (* k -1/2) 1/2))

rewrite360.0ms (2.1%)

Algorithm
batch-egg-rewrite
Rules
1130×log1p-expm1-u
538×expm1-log1p-u
246×prod-diff
158×pow1
156×add-exp-log
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
027218
1385214
24819214
Stop Event
node limit
Counts
7 → 273
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(*.f64 (PI.f64) n)
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (*.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))
Outputs
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (cbrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (/.f64 #s(literal 1 binary64) k)) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))) #s(literal 2 binary64))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(log.f64 (exp.f64 (pow.f64 k #s(literal -1/2 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 k #s(literal -1/2 binary64)))))
(cbrt.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64))))
(log1p.f64 (expm1.f64 (pow.f64 k #s(literal -1/2 binary64))))
(exp.f64 (neg.f64 (log.f64 (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (sqrt.f64 k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n))
(*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))) (cbrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) n))
(*.f64 (cbrt.f64 (pow.f64 n #s(literal 2 binary64))) (*.f64 (cbrt.f64 n) (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) n))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64))) (cbrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (cbrt.f64 (pow.f64 n #s(literal 2 binary64)))) (cbrt.f64 n))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n))
(*.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (*.f64 n (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(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)) n) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (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 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (/.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 (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 (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 (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (/.f64 (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))))) (sqrt.f64 k)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (*.f64 (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 k #s(literal -1/2 binary64))))
(*.f64 (cbrt.f64 (/.f64 #s(literal 1 binary64) k)) (*.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) k)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.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)))) (cbrt.f64 (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)))) #s(literal 1 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 k #s(literal 1/2 binary64)))) (cbrt.f64 k)) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (cbrt.f64 (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 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) #s(literal 1 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))))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (pow.f64 k #s(literal 1/4 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 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
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(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
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(*.f64 (/.f64 (pow.f64 (cbrt.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)))) #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
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(exp.f64 (log.f64 (/.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))))
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simplify139.0ms (0.8%)

Algorithm
egg-herbie
Rules
813×times-frac
737×fma-define
467×associate-*r*
392×associate-*l*
319×exp-prod
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
066419375
1137818177
2411418065
Stop Event
node limit
Counts
405 → 361
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
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(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) k))
(log.f64 (exp.f64 (/.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))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.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)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.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))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (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) (*.f64 (PI.f64) n)) (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) (*.f64 (PI.f64) n)) (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) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 1 binary64)))
Outputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))
(*.f64 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 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (fma.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)))) k)
(/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (fma.f64 k (fma.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))) #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)))) k)
(/.f64 (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (fma.f64 k (fma.f64 k (fma.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 3 binary64))) #s(literal -1/48 binary64)) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))) #s(literal 1/8 binary64)))) (*.f64 (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (*.f64 k (PI.f64)) n)))) k)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(exp.f64 (*.f64 #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 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 #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 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
(exp.f64 (*.f64 #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 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
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(*.f64 (*.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 (/.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (*.f64 (cbrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (*.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 (pow.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (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 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (neg.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 k)))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (neg.f64 (neg.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 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 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))) (sqrt.f64 k))
(/.f64 (*.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))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (/.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))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (/.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 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 1 binary64))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 3 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))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 3 binary64)) #s(literal 1/3 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))) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 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))) (sqrt.f64 k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(neg.f64 (/.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 k))))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(neg.f64 (/.f64 (neg.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 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(log.f64 (exp.f64 (/.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 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.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 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)) #s(literal 3 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))) (sqrt.f64 k))
(cbrt.f64 (*.f64 (pow.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))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.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))) #s(literal 3 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (/.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))))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 #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 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #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 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))) #s(literal 1 binary64)))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))

eval149.0ms (0.9%)

Compiler

Compiled 7475 to 4946 computations (33.8% saved)

prune69.0ms (0.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New34912361
Fresh000
Picked202
Done000
Total35112363
Accuracy
100.0%
Counts
363 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
99.6%
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
99.7%
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
99.5%
(*.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.5%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
75.2%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
99.7%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
45.9%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
37.2%
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
37.2%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
90.5%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
Compiler

Compiled 410 to 332 computations (19% saved)

localize364.0ms (2.2%)

Localize:

Found 19 expressions with local error:

NewAccuracyProgram
99.6%
(*.f64 n (PI.f64))
99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
99.4%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
99.3%
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
99.8%
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
99.7%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
99.6%
(*.f64 (PI.f64) n)
99.8%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))
99.8%
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
99.6%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
90.7%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
99.7%
(*.f64 n (/.f64 (PI.f64) k))
99.6%
(/.f64 (PI.f64) k)
99.2%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
78.3%
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
100.0%
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
99.8%
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
99.8%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
99.6%
(*.f64 (PI.f64) n)
Results
207.0ms193×256valid
70.0ms63×256infinite
Compiler

Compiled 238 to 125 computations (47.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 215.0ms
ival-pow: 98.0ms (45.5% of total)
ival-mult: 63.0ms (29.3% of total)
ival-sqrt: 22.0ms (10.2% of total)
ival-div: 11.0ms (5.1% of total)
const: 11.0ms (5.1% of total)
ival-sub: 9.0ms (4.2% of total)
ival-pi: 1.0ms (0.5% of total)

series100.0ms (0.6%)

Counts
16 → 292
Calls
Call 1
Inputs
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))>
#<alt (/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))>
#<alt (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))>
#<alt (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (PI.f64) k)>
#<alt (*.f64 n (/.f64 (PI.f64) k))>
#<alt (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))>
#<alt (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))>
#<alt (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)>
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))>
#<alt (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))>
#<alt (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 n (PI.f64))>
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)))>
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#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
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#<alt (*.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)))))>
Calls

81 calls:

TimeVariablePointExpression
40.0ms
n
@0
(pow (* 2 (* (PI) n)) (- 1/2 (* k 1/2)))
4.0ms
n
@-inf
(/ (* (pow (* 2 (* (PI) n)) (* k -1/2)) (sqrt (* 2 (* (PI) n)))) (sqrt k))
2.0ms
n
@inf
(* n (/ (PI) k))
2.0ms
n
@inf
(/ (* (pow (* 2 (* (PI) n)) (* k -1/2)) (sqrt (* 2 (* (PI) n)))) (sqrt k))
2.0ms
n
@0
(/ (* (pow (* 2 (* (PI) n)) (* k -1/2)) (sqrt (* 2 (* (PI) n)))) (sqrt k))

rewrite167.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
338×associate-*r*
301×log1p-expm1-u
301×expm1-log1p-u
291×pow1
291×add-cube-cbrt
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
042612
1758481
Stop Event
node limit
Counts
16 → 757
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (PI.f64) k)
(*.f64 n (/.f64 (PI.f64) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(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) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 n (PI.f64))
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)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.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 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(fabs.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.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))) #s(literal 3/2 binary64)))
(cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (log.f64 (sqrt.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 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (pow.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (cbrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (/.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) n) (*.f64 (+.f64 k #s(literal 1 binary64)) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (sqrt.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 k))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) #s(literal -1 binary64))
(neg.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k))))
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simplify505.0ms (3%)

Algorithm
egg-herbie
Rules
931×fma-define
476×times-frac
416×*-commutative
375×associate-/l*
341×associate-*r/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0126850570
1274949603
2752149335
Stop Event
node limit
Counts
1049 → 783
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)))))
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(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.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 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(fabs.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.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))) #s(literal 3/2 binary64)))
(cbrt.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3/2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(exp.f64 (log.f64 (sqrt.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 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (cbrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (pow.f64 k #s(literal -1/4 binary64)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal 1 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (/.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (cbrt.f64 #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #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 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3/2 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3/2 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) #s(literal 1 binary64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (cbrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) n)
(*.f64 (*.f64 n #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 n) #s(literal 2 binary64))) (cbrt.f64 n))
(*.f64 (*.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 n)) (sqrt.f64 (PI.f64)))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(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)))
Outputs
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(*.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 (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 (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 (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 (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 (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 (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 (sqrt.f64 #s(literal 2 binary64)) (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)))))
(*.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)))))
(*.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)))))
(*.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)))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 (*.f64 k #s(literal -1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 (*.f64 k #s(literal -1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 (*.f64 k #s(literal -1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 (*.f64 k #s(literal -1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.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))))))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 (*.f64 k #s(literal -1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.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))))))) (sqrt.f64 #s(literal 2 binary64))))
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(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.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))))))) (sqrt.f64 #s(literal 2 binary64))))
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(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))) #s(literal 1 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64)) (cbrt.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 n (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) n)
(*.f64 n (PI.f64))
(*.f64 (*.f64 n #s(literal 1 binary64)) (PI.f64))
(*.f64 n (PI.f64))
(*.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 n) #s(literal 2 binary64))) (cbrt.f64 n))
(*.f64 n (PI.f64))
(*.f64 (*.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
(*.f64 n (PI.f64))
(*.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 n (PI.f64))
(*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 n (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
(*.f64 n (PI.f64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64))
(*.f64 n (PI.f64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 3 binary64))
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(fabs.f64 (*.f64 n (PI.f64)))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 n (PI.f64))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (PI.f64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(*.f64 n (PI.f64))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (PI.f64) n))))
(*.f64 n (PI.f64))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(*.f64 n (PI.f64))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal 1 binary64)))
(*.f64 n (PI.f64))

eval424.0ms (2.5%)

Compiler

Compiled 19178 to 11697 computations (39% saved)

prune168.0ms (1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New995121007
Fresh707
Picked325
Done000
Total1005141019
Accuracy
100.0%
Counts
1019 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.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))
46.1%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
46.0%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
91.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
46.0%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
45.9%
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
37.2%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
37.2%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
37.2%
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
37.2%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
90.5%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
90.3%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
Compiler

Compiled 335 to 272 computations (18.8% saved)

localize259.0ms (1.5%)

Localize:

Found 18 expressions with local error:

NewAccuracyProgram
99.6%
(*.f64 (PI.f64) n)
99.3%
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))
99.2%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
78.3%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n))))
99.8%
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
99.6%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
99.4%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
99.6%
(/.f64 n (/.f64 k (PI.f64)))
99.6%
(/.f64 k (PI.f64))
99.2%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
78.3%
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
100.0%
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
99.6%
(/.f64 n (/.f64 k (PI.f64)))
99.6%
(/.f64 k (PI.f64))
78.0%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
99.8%
(/.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))
99.8%
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
99.6%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
Results
144.0ms193×256valid
47.0ms63×256infinite
Compiler

Compiled 180 to 87 computations (51.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 137.0ms
ival-mult: 50.0ms (36.5% of total)
ival-pow: 38.0ms (27.7% of total)
ival-sqrt: 23.0ms (16.8% of total)
ival-div: 18.0ms (13.1% of total)
ival-sub: 4.0ms (2.9% of total)
const: 4.0ms (2.9% of total)
ival-pi: 1.0ms (0.7% of total)

series30.0ms (0.2%)

Counts
15 → 300
Calls
Call 1
Inputs
#<alt (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))>
#<alt (/.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))>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))>
#<alt (/.f64 k (PI.f64))>
#<alt (/.f64 n (/.f64 k (PI.f64)))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))>
#<alt (sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 k (PI.f64))>
#<alt (/.f64 n (/.f64 k (PI.f64)))>
#<alt (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))>
#<alt (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))>
Outputs
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 k (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))>
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) k))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
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#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (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 (*.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 (*.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)>
Calls

81 calls:

TimeVariablePointExpression
3.0ms
k
@-inf
(/ n (/ k (PI)))
1.0ms
k
@-inf
(sqrt (* 2 (/ n (/ k (PI)))))
1.0ms
k
@0
(pow (* n (* 2 (PI))) (- 1/2 (/ k 2)))
1.0ms
k
@0
(/ (pow (* n (* 2 (PI))) (- 1/2 (/ k 2))) (sqrt k))
0.0ms
n
@-inf
(sqrt (* 2 (/ n (/ k (PI)))))

rewrite236.0ms (1.4%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
035401
1593401
27178401
Stop Event
node limit
Counts
15 → 867
Calls
Call 1
Inputs
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(/.f64 k (PI.f64))
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 k (PI.f64))
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))
Outputs
(-.f64 (exp.f64 (log1p.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))))) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (cbrt.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)))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (cbrt.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)))))
(*.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(*.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (pow.f64 (PI.f64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (neg.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
(pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))
(pow.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))) #s(literal 1 binary64))
(pow.f64 (cbrt.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)))) #s(literal 3 binary64))
(pow.f64 (pow.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))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
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(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (/.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
(fabs.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 n (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 (*.f64 n (PI.f64)) k) #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) (*.f64 n (PI.f64)))))
(*.f64 (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (/.f64 (cbrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (*.f64 (cbrt.f64 n) (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)))
(*.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))
(*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (/.f64 n (sqrt.f64 k)))
(*.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 (PI.f64) k))
(*.f64 (/.f64 n (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (PI.f64) (cbrt.f64 k)))
(*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 n k))
(*.f64 (/.f64 (PI.f64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 n (cbrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (*.f64 n (PI.f64)) (cbrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (/.f64 n (cbrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 n (sqrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) k) (/.f64 (cbrt.f64 n) (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (cbrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (/.f64 (sqrt.f64 n) k) (/.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (cbrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) (*.f64 n (PI.f64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (/.f64 n k) #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 n (neg.f64 k)) (neg.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 k)) (*.f64 n (neg.f64 (PI.f64))))
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 k) (*.f64 n (PI.f64))))
(/.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 k (PI.f64)))))
(/.f64 (*.f64 n (neg.f64 (PI.f64))) (neg.f64 k))
(/.f64 (neg.f64 n) (/.f64 k (neg.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(/.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (*.f64 (sqrt.f64 n) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 (neg.f64 (neg.f64 n)) (/.f64 k (PI.f64)))
(/.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 k (PI.f64)))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))
(/.f64 (/.f64 n (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64)) k)
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 k))
(/.f64 (/.f64 n (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 k (PI.f64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 2 binary64))
(pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1 binary64))
(pow.f64 (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(neg.f64 (/.f64 n (/.f64 k (neg.f64 (PI.f64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(neg.f64 (/.f64 (neg.f64 n) (/.f64 k (PI.f64))))
(sqrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(log.f64 (exp.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (/.f64 k (PI.f64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(exp.f64 (log.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 k)))

simplify279.0ms (1.7%)

Algorithm
egg-herbie
Rules
512×cube-prod
472×fma-define
468×exp-prod
441×*-commutative
308×associate-*r/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
093941683
1193640620
2566139980
Stop Event
node limit
Counts
1167 → 529
Calls
Call 1
Inputs
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
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(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal -1/2 binary64))))
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(*.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.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)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (cbrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (cbrt.f64 (/.f64 #s(literal 1 binary64) k))) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))
(fabs.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))))))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 n (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 (*.f64 n (PI.f64)) k) #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 1 binary64) k))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 k) (*.f64 n (PI.f64)))))
(*.f64 (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64))) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (/.f64 (cbrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (*.f64 (cbrt.f64 n) (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)))
(*.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))
(*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (/.f64 n (sqrt.f64 k)))
(*.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 (PI.f64) k))
(*.f64 (/.f64 n (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (PI.f64) (cbrt.f64 k)))
(*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 n k))
(*.f64 (/.f64 (PI.f64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 n (cbrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (*.f64 n (PI.f64)) (cbrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (/.f64 n (cbrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 n (sqrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) k) (/.f64 (cbrt.f64 n) (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (cbrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (/.f64 (sqrt.f64 n) k) (/.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (cbrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) (*.f64 n (PI.f64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (/.f64 n k) #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 n (neg.f64 k)) (neg.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 k)) (*.f64 n (neg.f64 (PI.f64))))
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 k) (*.f64 n (PI.f64))))
(/.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 k (PI.f64)))))
(/.f64 (*.f64 n (neg.f64 (PI.f64))) (neg.f64 k))
(/.f64 (neg.f64 n) (/.f64 k (neg.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(/.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (*.f64 (sqrt.f64 n) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 (neg.f64 (neg.f64 n)) (/.f64 k (PI.f64)))
(/.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 k (PI.f64)))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))
(/.f64 (/.f64 n (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64)) k)
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 k))
(/.f64 (/.f64 n (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 k (PI.f64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 2 binary64))
(pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1 binary64))
(pow.f64 (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(neg.f64 (/.f64 n (/.f64 k (neg.f64 (PI.f64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(neg.f64 (/.f64 (neg.f64 n) (/.f64 k (PI.f64))))
(sqrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(log.f64 (exp.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (/.f64 k (PI.f64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(exp.f64 (log.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 k)))
Outputs
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (*.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 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (*.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 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (*.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 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
(pow.f64 (*.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 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))
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(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (/.f64 (/.f64 k n) (PI.f64)))) #s(literal 1 binary64)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 k n) (PI.f64))) #s(literal 2 binary64)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1/4 binary64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (/.f64 n (sqrt.f64 k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 n (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (PI.f64) (cbrt.f64 k)))
(*.f64 n (/.f64 (/.f64 (PI.f64) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 n k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (PI.f64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 n (cbrt.f64 k)))
(*.f64 n (/.f64 (/.f64 (PI.f64) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (*.f64 n (PI.f64)) (cbrt.f64 k)))
(*.f64 n (/.f64 (/.f64 (PI.f64) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 k)))
(*.f64 n (/.f64 (/.f64 (PI.f64) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 k)))
(*.f64 n (/.f64 (/.f64 (PI.f64) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (/.f64 n (cbrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 n (sqrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) k) (/.f64 (cbrt.f64 n) (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 (cbrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (sqrt.f64 n) k) (/.f64 (sqrt.f64 n) (/.f64 #s(literal 1 binary64) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (/.f64 k (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (cbrt.f64 (/.f64 k (PI.f64)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 4 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1 binary64)) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (*.f64 n (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) (sqrt.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (*.f64 (/.f64 n k) #s(literal 1 binary64)) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (*.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 n (neg.f64 k)) (neg.f64 (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 k)) (*.f64 n (neg.f64 (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 k) (*.f64 n (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 (/.f64 k (PI.f64)))))
(/.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))) (sqrt.f64 (/.f64 k (PI.f64)))))
(/.f64 (*.f64 n (neg.f64 (PI.f64))) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (neg.f64 n) (/.f64 k (neg.f64 (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (/.f64 n k) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (*.f64 (sqrt.f64 n) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(/.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))) (sqrt.f64 (/.f64 k (PI.f64)))))
(/.f64 (neg.f64 (neg.f64 n)) (/.f64 k (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 k (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (/.f64 n (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 k (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (/.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 n)) (sqrt.f64 (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (sqrt.f64 (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))) (cbrt.f64 k))
(*.f64 n (/.f64 (/.f64 (PI.f64) (cbrt.f64 k)) (cbrt.f64 (pow.f64 k #s(literal 2 binary64)))))
(/.f64 (/.f64 n (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 k (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(*.f64 (PI.f64) (/.f64 n k))
(pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 2 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(pow.f64 (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(pow.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(pow.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 (PI.f64) (/.f64 n k))
(neg.f64 (/.f64 n (/.f64 k (neg.f64 (PI.f64)))))
(*.f64 (PI.f64) (/.f64 n k))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(*.f64 (PI.f64) (/.f64 n k))
(neg.f64 (/.f64 (neg.f64 n) (/.f64 k (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(sqrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(*.f64 (PI.f64) (/.f64 n k))
(log.f64 (exp.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (PI.f64) (/.f64 n k))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(*.f64 (PI.f64) (/.f64 n k))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 3 binary64)))
(*.f64 (PI.f64) (/.f64 n k))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(*.f64 (PI.f64) (/.f64 n k))
(cbrt.f64 (/.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (/.f64 k (PI.f64)) #s(literal 3 binary64))))
(*.f64 (PI.f64) (/.f64 n k))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (PI.f64) (/.f64 n k))
(exp.f64 (log.f64 (/.f64 (*.f64 n (PI.f64)) k)))
(*.f64 (PI.f64) (/.f64 n k))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1 binary64)))
(*.f64 (PI.f64) (/.f64 n k))
(exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 n (PI.f64)))) #s(literal -1 binary64)))
(*.f64 (PI.f64) (/.f64 n k))
(exp.f64 (-.f64 (log.f64 (*.f64 n (PI.f64))) (log.f64 k)))
(*.f64 (PI.f64) (/.f64 n k))

eval340.0ms (2%)

Compiler

Compiled 14254 to 8397 computations (41.1% saved)

prune223.0ms (1.3%)

Pruning

30 alts after pruning (24 fresh and 6 done)

PrunedKeptTotal
New88319902
Fresh257
Picked145
Done022
Total88630916
Accuracy
100.0%
Counts
916 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
25.5%
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
36.8%
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
99.6%
(/.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))
46.1%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
46.1%
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
37.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
46.0%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
91.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
37.5%
(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
46.0%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
37.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
45.9%
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
37.2%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
37.2%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
90.5%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
36.9%
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
36.9%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
36.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
36.9%
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
37.0%
(sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
90.3%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
34.6%
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
27.1%
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
27.1%
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))
Compiler

Compiled 666 to 548 computations (17.7% saved)

localize324.0ms (1.9%)

Localize:

Found 20 expressions with local error:

NewAccuracyProgram
99.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
99.8%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
99.7%
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
49.7%
(PI.f64)
99.9%
(sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))
99.8%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
99.8%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
49.7%
(PI.f64)
99.8%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))
99.8%
(/.f64 k (PI.f64))
90.7%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
49.7%
(PI.f64)
99.8%
(*.f64 (/.f64 (PI.f64) k) n)
99.8%
(/.f64 (PI.f64) k)
90.7%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
49.7%
(PI.f64)
99.8%
(*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))
99.8%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
91.5%
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
49.7%
(PI.f64)
Results
126.0ms133×256unsamplable
103.0ms121×256valid
2.0ms256infinite
Compiler

Compiled 199 to 110 computations (44.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 176.0ms
ival-mult: 74.0ms (42% of total)
ival-pow: 42.0ms (23.8% of total)
ival-div: 31.0ms (17.6% of total)
ival-sqrt: 17.0ms (9.6% of total)
ival-sub: 7.0ms (4% of total)
const: 4.0ms (2.3% of total)
ival-pi: 1.0ms (0.6% of total)

series35.0ms (0.2%)

Counts
14 → 216
Calls
Call 1
Inputs
#<alt (PI.f64)>
#<alt (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (PI.f64)>
#<alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))>
#<alt (*.f64 (/.f64 (PI.f64) k) n)>
#<alt (PI.f64)>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))>
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))>
#<alt (PI.f64)>
#<alt (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))>
#<alt (PI.f64)>
#<alt (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))>
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))>
Outputs
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))>
#<alt (+.f64 (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k (*.f64 n (PI.f64))))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))))))>
#<alt (+.f64 (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k (*.f64 n (PI.f64))))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (/.f64 (+.f64 (*.f64 #s(literal -1/12 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))))) (+.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64))))))))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))))))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #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 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) k)>
#<alt (/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (-.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64))))) (/.f64 (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) (*.f64 k (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))) k)>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
Calls

54 calls:

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

rewrite238.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
289×prod-diff
226×log1p-expm1-u
226×expm1-log1p-u
224×add-exp-log
224×pow1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
032316
1571310
27666310
Stop Event
node limit
Counts
14 → 718
Calls
Call 1
Inputs
(PI.f64)
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(PI.f64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(*.f64 (/.f64 (PI.f64) k) n)
(PI.f64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(PI.f64)
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(PI.f64)
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
Outputs
(-.f64 (exp.f64 (log1p.f64 (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)) (cbrt.f64 (*.f64 (PI.f64) (PI.f64))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (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 (*.f64 (PI.f64) (PI.f64)))
(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)))
(PI.f64)
(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 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64))
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(*.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) k)))))
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(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(/.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(/.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal -2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(fabs.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))))))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 3/2 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal -1 binary64)))

simplify252.0ms (1.5%)

Algorithm
egg-herbie
Rules
648×associate-*r*
619×associate-*l*
434×times-frac
431×*-commutative
364×associate-*r/
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
098837350
1218235769
2795335769
Stop Event
node limit
Counts
934 → 541
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k (*.f64 n (PI.f64))))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k (*.f64 n (PI.f64))))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 k (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (/.f64 (+.f64 (*.f64 #s(literal -1/12 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64))))))) (+.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64))))))))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 k (exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) k)
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(fabs.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))) (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))))
(*.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.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)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)) (sqrt.f64 n))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 n) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)))
(*.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (cbrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 (*.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(/.f64 (cbrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(/.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal -2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))) #s(literal -1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(fabs.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))))))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 3/2 binary64)) (pow.f64 k #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal -1 binary64)))
Outputs
(*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (*.f64 n (PI.f64)))) (*.f64 (/.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/4 binary64))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 k (*.f64 n (PI.f64))))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))))))
(fma.f64 (pow.f64 k #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (*.f64 k (*.f64 n (PI.f64)))) (*.f64 (/.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 n (PI.f64))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))) k))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
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(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
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(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal 1 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))) #s(literal -1 binary64)))
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eval386.0ms (2.3%)

Compiler

Compiled 18392 to 11794 computations (35.9% saved)

prune242.0ms (1.4%)

Pruning

43 alts after pruning (32 fresh and 11 done)

PrunedKeptTotal
New1160161176
Fresh31619
Picked055
Done066
Total1163431206
Accuracy
100.0%
Counts
1206 → 43
Alt Table
Click to see full alt table
StatusAccuracyProgram
25.5%
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
36.7%
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
25.5%
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
91.2%
(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64))
37.7%
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
37.7%
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
99.6%
(/.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))
46.1%
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
46.1%
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
37.6%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
45.9%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
46.0%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
36.9%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
37.5%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
46.0%
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) n))))
91.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
37.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
37.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
37.5%
(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
46.0%
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
37.5%
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
45.9%
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
46.0%
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
37.2%
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
37.2%
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
46.0%
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
90.5%
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
36.9%
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
36.9%
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
36.9%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
36.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
36.9%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k) (*.f64 n #s(literal 2 binary64)))))
36.9%
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
37.0%
(sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
90.3%
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
36.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
34.6%
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
27.1%
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)))
27.1%
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
27.1%
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))
Compiler

Compiled 1226 to 865 computations (29.4% saved)

regimes71.0ms (0.4%)

Counts
61 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(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 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) 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))
(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (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 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 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (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 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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)))) (sqrt.f64 k)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
Outputs
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (sqrt.f64 k))
Calls

4 calls:

20.0ms
n
18.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
17.0ms
k
11.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.7%1k
99.7%1n
99.7%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.7%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 25 computations (19.4% saved)

regimes72.0ms (0.4%)

Counts
58 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(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 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) 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))
(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (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 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 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (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 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
Outputs
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
Calls

4 calls:

20.0ms
n
18.0ms
k
18.0ms
(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
Results
AccuracySegmentsBranch
99.6%1(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
99.6%1k
99.6%1n
99.6%1(*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)
Compiler

Compiled 31 to 25 computations (19.4% saved)

regimes45.0ms (0.3%)

Counts
47 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(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 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) 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))
(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
Outputs
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64))
Calls

2 calls:

26.0ms
k
15.0ms
n
Results
AccuracySegmentsBranch
99.6%2k
91.2%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes37.0ms (0.2%)

Counts
45 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(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 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) 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 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
Calls

1 calls:

33.0ms
k
Results
AccuracySegmentsBranch
99.6%2k
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes37.0ms (0.2%)

Counts
44 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(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 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))))
(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (*.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
Outputs
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
Calls

2 calls:

21.0ms
n
13.0ms
k
Results
AccuracySegmentsBranch
46.1%1n
46.1%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts
26 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(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 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
Outputs
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
Calls

2 calls:

8.0ms
n
7.0ms
k
Results
AccuracySegmentsBranch
46.1%1n
46.1%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes19.0ms (0.1%)

Counts
25 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(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 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) n) (PI.f64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (neg.f64 n) (/.f64 #s(literal 1 binary64) (/.f64 k (neg.f64 (PI.f64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) k) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
Outputs
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
Calls

2 calls:

8.0ms
k
8.0ms
n
Results
AccuracySegmentsBranch
46.0%1n
46.0%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes24.0ms (0.1%)

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

2 calls:

16.0ms
n
6.0ms
k
Results
AccuracySegmentsBranch
46.0%1n
46.0%1k
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

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

2 calls:

7.0ms
k
5.0ms
n
Results
AccuracySegmentsBranch
37.7%1k
37.7%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0%)

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

2 calls:

4.0ms
k
3.0ms
n
Results
AccuracySegmentsBranch
37.7%1k
37.7%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts
7 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(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 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n)))
Outputs
(sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
Calls

2 calls:

3.0ms
n
3.0ms
k
Results
AccuracySegmentsBranch
37.0%1k
37.0%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Counts
3 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(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)))
Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
Calls

2 calls:

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

Compiled 6 to 4 computations (33.3% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

2 calls:

1.0ms
k
0.0ms
n
Results
AccuracySegmentsBranch
36.9%1k
36.9%1n
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch4.0ms (0%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
3.0ms
2.8003659615743843e-19
3.015080809951096e-19
Results
2.0ms16×0valid
Compiler

Compiled 51 to 42 computations (17.6% saved)

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

bsearch23.0ms (0.1%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
21.0ms
4.756002203607135e-40
7.018235869649084e-38
Results
16.0ms112×0valid
Compiler

Compiled 212 to 173 computations (18.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-pow: 3.0ms (29.3% of total)
ival-div: 2.0ms (19.5% of total)
ival-mult: 2.0ms (19.5% of total)
ival-sqrt: 2.0ms (19.5% of total)
ival-sub: 1.0ms (9.8% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
073612
1102612
2114612
3120612
4124612
5125612
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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))
(if (<=.f64 k #s(literal 6230756230241793/20769187434139310514121985316880384 binary64)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k)) (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 1225996432692711/383123885216472214589586756787577295904684780545900544 binary64)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
Outputs
(/.f64 (*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) (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))
(if (<=.f64 k #s(literal 6230756230241793/20769187434139310514121985316880384 binary64)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k)) (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 6230756230241793/20769187434139310514121985316880384 binary64)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k)) (pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 1225996432692711/383123885216472214589586756787577295904684780545900544 binary64)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 k (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 n (/.f64 (PI.f64) k))))

soundness1.7s (10%)

Rules
1130×log1p-expm1-u
813×times-frac
737×fma-define
648×associate-*r*
619×associate-*l*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
035401
1593401
27178401
066419375
1137818177
2411418065
098837350
1218235769
2795335769
039438
196380
2211380
3410364
4686352
51171352
61433352
71698352
82017352
92060352
102088352
112099352
122101352
032316
1571310
27666310
042612
1758481
027218
1385214
24819214
Stop Event
fuel
node limit
node limit
node limit
saturated
node limit
node limit
node limit
Compiler

Compiled 1329 to 848 computations (36.2% saved)

preprocess110.0ms (0.7%)

Compiler

Compiled 364 to 234 computations (35.7% saved)

end0.0ms (0%)

Profiling

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