Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}
double f(double x, double y) {
        double r763941 = x;
        double r763942 = y;
        double r763943 = r763942 * r763942;
        double r763944 = exp(r763943);
        double r763945 = r763941 * r763944;
        return r763945;
}
↓
double f(double x, double y) {
        double r763946 = x;
        double r763947 = y;
        double r763948 = r763947 * r763947;
        double r763949 = exp(r763948);
        double r763950 = sqrt(r763949);
        double r763951 = r763946 * r763950;
        double r763952 = exp(r763947);
        double r763953 = 2.0;
        double r763954 = r763947 / r763953;
        double r763955 = pow(r763952, r763954);
        double r763956 = r763951 * r763955;
        return r763956;
}

Error

Bits error versus x

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

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

  6. Applied add-log-exp0.0

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

  7. Applied exp-to-pow0.0

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

  8. Applied sqrt-pow10.0

    \[\leadsto \left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \color{blue}{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\]

  9. Final simplification0.0

    \[\leadsto \left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]

Reproduce

herbie shell --seed 2020083 
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"
  :precision binary64

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

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