Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \left(\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}} \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right)\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \left(\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}} \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right)\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}
double f(double x, double y) {
        double r923166 = x;
        double r923167 = y;
        double r923168 = r923167 * r923167;
        double r923169 = exp(r923168);
        double r923170 = r923166 * r923169;
        return r923170;
}
↓
double f(double x, double y) {
        double r923171 = x;
        double r923172 = y;
        double r923173 = exp(r923172);
        double r923174 = 2.0;
        double r923175 = r923172 / r923174;
        double r923176 = pow(r923173, r923175);
        double r923177 = cbrt(r923176);
        double r923178 = r923177 * r923177;
        double r923179 = r923178 * r923177;
        double r923180 = r923171 * r923179;
        double r923181 = r923180 * r923176;
        return r923181;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 sqr-pow0.0

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

  7. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(x \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.0

    \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}} \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right)}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]

  10. Final simplification0.0

    \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}} \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right)\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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))))