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

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.1

$e^{\log x \cdot \log y}$
2. Using strategy rm

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

$\leadsto e^{\log \color{blue}{\left({x}^{\left(\log y\right)}\right)}}$
5. Using strategy rm

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