Average Error: 0.0 → 0.0
Time: 13.9s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}\right) \cdot {\left(\sqrt[3]{e^{y}}\right)}^{y}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}\right) \cdot {\left(\sqrt[3]{e^{y}}\right)}^{y}
double f(double x, double y) {
        double r560466 = x;
        double r560467 = y;
        double r560468 = r560467 * r560467;
        double r560469 = exp(r560468);
        double r560470 = r560466 * r560469;
        return r560470;
}
↓
double f(double x, double y) {
        double r560471 = x;
        double r560472 = y;
        double r560473 = exp(r560472);
        double r560474 = cbrt(r560473);
        double r560475 = r560474 * r560474;
        double r560476 = pow(r560475, r560472);
        double r560477 = r560471 * r560476;
        double r560478 = pow(r560474, r560472);
        double r560479 = r560477 * r560478;
        return r560479;
}

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-cube-cbrt0.0

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

  7. Applied unpow-prod-down0.0

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

  8. Applied associate-*r*0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 
(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))))