Average Error: 0.0 → 0.1
Time: 16.7s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot \sqrt[3]{{\left(e^{y}\right)}^{y} \cdot \left({\left(e^{y}\right)}^{y} \cdot e^{y \cdot y}\right)}\]
x \cdot e^{y \cdot y}
↓
x \cdot \sqrt[3]{{\left(e^{y}\right)}^{y} \cdot \left({\left(e^{y}\right)}^{y} \cdot e^{y \cdot y}\right)}
double f(double x, double y) {
        double r36259503 = x;
        double r36259504 = y;
        double r36259505 = r36259504 * r36259504;
        double r36259506 = exp(r36259505);
        double r36259507 = r36259503 * r36259506;
        return r36259507;
}
↓
double f(double x, double y) {
        double r36259508 = x;
        double r36259509 = y;
        double r36259510 = exp(r36259509);
        double r36259511 = pow(r36259510, r36259509);
        double r36259512 = r36259509 * r36259509;
        double r36259513 = exp(r36259512);
        double r36259514 = r36259511 * r36259513;
        double r36259515 = r36259511 * r36259514;
        double r36259516 = cbrt(r36259515);
        double r36259517 = r36259508 * r36259516;
        return r36259517;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.1
\[x \cdot {\left(e^{y}\right)}^{y}\]

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-cbrt-cube0.1

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

  8. Applied pow-exp0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 +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))))