Average Error: 0.0 → 0.0
Time: 21.1s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \sqrt{{\left(e^{y}\right)}^{y}}\right) \cdot \sqrt{{\left(e^{y}\right)}^{y}}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \sqrt{{\left(e^{y}\right)}^{y}}\right) \cdot \sqrt{{\left(e^{y}\right)}^{y}}
double f(double x, double y) {
        double r264456059 = x;
        double r264456060 = y;
        double r264456061 = r264456060 * r264456060;
        double r264456062 = exp(r264456061);
        double r264456063 = r264456059 * r264456062;
        return r264456063;
}
↓
double f(double x, double y) {
        double r264456064 = x;
        double r264456065 = y;
        double r264456066 = exp(r264456065);
        double r264456067 = pow(r264456066, r264456065);
        double r264456068 = sqrt(r264456067);
        double r264456069 = r264456064 * r264456068;
        double r264456070 = r264456069 * r264456068;
        return r264456070;
}

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-log-exp0.0

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

  4. Applied exp-to-pow0.0

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

  6. Applied add-sqr-sqrt0.0

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

  7. Applied associate-*r*0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 
(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))))