Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\sqrt{e^{\left(\sqrt[3]{\left(x \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}}} \cdot \sqrt{e^{\left(x \cdot y\right) \cdot y}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
\sqrt{e^{\left(\sqrt[3]{\left(x \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}}} \cdot \sqrt{e^{\left(x \cdot y\right) \cdot y}}
double f(double x, double y) {
        double r189056 = x;
        double r189057 = y;
        double r189058 = r189056 * r189057;
        double r189059 = r189058 * r189057;
        double r189060 = exp(r189059);
        return r189060;
}
↓
double f(double x, double y) {
        double r189061 = x;
        double r189062 = y;
        double r189063 = r189061 * r189062;
        double r189064 = r189063 * r189062;
        double r189065 = cbrt(r189064);
        double r189066 = r189065 * r189065;
        double r189067 = r189066 * r189065;
        double r189068 = exp(r189067);
        double r189069 = sqrt(r189068);
        double r189070 = exp(r189064);
        double r189071 = sqrt(r189070);
        double r189072 = r189069 * r189071;
        return r189072;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

    \[e^{\left(x \cdot y\right) \cdot y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt{e^{\left(x \cdot y\right) \cdot y}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020056 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))