Average Error: 0.1 → 0.1
Time: 39.4s
Precision: 64
Internal Precision: 576
\[e^{\log x \cdot \log y}\]
\[\left(\sqrt[3]{{x}^{\left(\log y\right)}} \cdot \sqrt[3]{{x}^{\left(\log y\right)}}\right) \cdot \sqrt[3]{{y}^{\left(\log x\right)}}\]

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[e^{\log x \cdot \log y}\]
  2. Using strategy rm
  3. Applied add-log-exp0.1

    \[\leadsto e^{\color{blue}{\log \left(e^{\log x \cdot \log y}\right)}}\]
  4. Applied simplify0.1

    \[\leadsto e^{\log \color{blue}{\left({x}^{\left(\log y\right)}\right)}}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt0.1

    \[\leadsto \color{blue}{\left(\sqrt[3]{e^{\log \left({x}^{\left(\log y\right)}\right)}} \cdot \sqrt[3]{e^{\log \left({x}^{\left(\log y\right)}\right)}}\right) \cdot \sqrt[3]{e^{\log \left({x}^{\left(\log y\right)}\right)}}}\]
  7. Applied simplify0.1

    \[\leadsto \color{blue}{\left(\sqrt[3]{{x}^{\left(\log y\right)}} \cdot \sqrt[3]{{x}^{\left(\log y\right)}}\right)} \cdot \sqrt[3]{e^{\log \left({x}^{\left(\log y\right)}\right)}}\]
  8. Applied simplify0.1

    \[\leadsto \left(\sqrt[3]{{x}^{\left(\log y\right)}} \cdot \sqrt[3]{{x}^{\left(\log y\right)}}\right) \cdot \color{blue}{\sqrt[3]{{y}^{\left(\log x\right)}}}\]

Runtime

Time bar (total: 39.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x y)
  :name "exp(log(x)*log(y))"
  (exp (* (log x) (log y))))