Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right)\]
x \cdot e^{y \cdot y}
↓
x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right)
double f(double x, double y) {
        double r970191 = x;
        double r970192 = y;
        double r970193 = r970192 * r970192;
        double r970194 = exp(r970193);
        double r970195 = r970191 * r970194;
        return r970195;
}
↓
double f(double x, double y) {
        double r970196 = x;
        double r970197 = y;
        double r970198 = exp(r970197);
        double r970199 = pow(r970198, r970197);
        double r970200 = log1p(r970199);
        double r970201 = expm1(r970200);
        double r970202 = r970196 * r970201;
        return r970202;
}

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 expm1-log1p-u0.0

    \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right)}\]

  7. Final simplification0.0

    \[\leadsto x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right)\]

Reproduce

herbie shell --seed 2019362 +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))))