Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot {\left(\sqrt[3]{e^{y}}\right)}^{y}\right) \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot {\left(\sqrt[3]{e^{y}}\right)}^{y}\right) \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}
double f(double x, double y) {
        double r547042 = x;
        double r547043 = y;
        double r547044 = r547043 * r547043;
        double r547045 = exp(r547044);
        double r547046 = r547042 * r547045;
        return r547046;
}
↓
double f(double x, double y) {
        double r547047 = x;
        double r547048 = y;
        double r547049 = exp(r547048);
        double r547050 = cbrt(r547049);
        double r547051 = pow(r547050, r547048);
        double r547052 = r547047 * r547051;
        double r547053 = r547050 * r547050;
        double r547054 = pow(r547053, r547048);
        double r547055 = r547052 * r547054;
        return r547055;
}

Error

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Bits error versus y

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Results

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Target

Original0.0
Target0.0
Herbie0.0
\[x \cdot {\left(e^{y}\right)}^{y}\]

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]

  2. Simplified0.0

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

  4. Applied add-cube-cbrt0.0

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

  5. Applied unpow-prod-down0.0

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

  6. Applied associate-*l*0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))