Migdal et al, Equation (51)

Time bar (total: 2.4s)

analyze85.0ms (3.5%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%50%0.1%0%50%0%2
50%25%25%0.1%0%50%0%3
50%25%25%0.1%0%50%0%4
50%25%25%0.1%0%50%0%5
53.3%25%21.9%0.1%0%53.1%0%6
57.1%25%18.7%0.1%0%54.6%1.6%7
61.5%25%15.6%0.1%0%57%2.3%8
65.3%25%13.3%0.1%0%58.1%3.5%9
68.8%25%11.3%0.1%0%59.5%4.1%10
71.5%25%10%0.1%0%60.2%4.8%11
73.8%25%8.9%0.1%0%60.9%5.1%12
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample2.1s (88.3%)

Results
977.0ms6214×body256valid
479.0ms1002×body1024invalid
366.0ms2042×body256infinite
132.0ms455×body512invalid
122.0ms1087×body256invalid
42.0ms193×body256unsamplable
Bogosity

preprocess198.0ms (8.2%)

Algorithm
1×egg-herbie
Rules
533×fma-def
488×*-commutative
402×associate-*r*
344×associate-/r*
325×associate-/l*
Problems
250×No Errors
6×(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
039438
1107380
2282380
3783364
42337356
54445352
66571352
Stop Event
1×node limit
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 (neg.f64 k)) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 1 k) 2)))
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 (neg.f64 k)) 2))))
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 1 k) 2))))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
Outputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 (neg.f64 k)) 2)))
(*.f64 (/.f64 1 (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 (neg.f64 k) 2))))
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 1 k) 2)) (sqrt.f64 (neg.f64 k)))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k 2))) (sqrt.f64 (neg.f64 k)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (+.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 (neg.f64 k)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 1/2 k 1/2)) (sqrt.f64 (neg.f64 k)))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 1/2)) (sqrt.f64 (neg.f64 k)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) (neg.f64 n))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n -2)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n -2)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n -2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 (neg.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 (neg.f64 k)) 2))))
(*.f64 (/.f64 1 (sqrt.f64 (neg.f64 k))) (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 (neg.f64 k) 2)))))
(/.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (+.f64 1 k) 2))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k 2)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (+.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 1/2 k 1/2))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 1/2))) (sqrt.f64 (neg.f64 k)))
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 1 k) 2))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) (neg.f64 n))) (/.f64 (-.f64 1 k) 2))))
(/.f64 (neg.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n -2)) (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n -2)) (fma.f64 -1/2 k 1/2))) (sqrt.f64 k))
(/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n -2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 n 2))))
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 n 2))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 2 (*.f64 k (PI.f64))) (+.f64 1/2 (/.f64 n -2))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 2 (*.f64 k (PI.f64))) (+.f64 1/2 (*.f64 -1/2 n))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (fma.f64 -1/2 n 1/2)) (sqrt.f64 n))
Compiler

Compiled 57 to 39 computations (31.6% saved)

end0.0ms (0%)

Profiling

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