Average Error: 0.0 → 0.1
Time: 3.5s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \left(\sqrt{e^{y \cdot y}} \cdot \left|\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}} \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right|\right)\right) \cdot \sqrt{\sqrt[3]{e^{y \cdot y}}}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \left(\sqrt{e^{y \cdot y}} \cdot \left|\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}} \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right|\right)\right) \cdot \sqrt{\sqrt[3]{e^{y \cdot y}}}
double f(double x, double y) {
        double r999317 = x;
        double r999318 = y;
        double r999319 = r999318 * r999318;
        double r999320 = exp(r999319);
        double r999321 = r999317 * r999320;
        return r999321;
}
↓
double f(double x, double y) {
        double r999322 = x;
        double r999323 = y;
        double r999324 = r999323 * r999323;
        double r999325 = exp(r999324);
        double r999326 = sqrt(r999325);
        double r999327 = cbrt(r999325);
        double r999328 = cbrt(r999327);
        double r999329 = r999328 * r999328;
        double r999330 = r999329 * r999328;
        double r999331 = fabs(r999330);
        double r999332 = r999326 * r999331;
        double r999333 = r999322 * r999332;
        double r999334 = sqrt(r999327);
        double r999335 = r999333 * r999334;
        return r999335;
}

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

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied sqrt-prod0.0

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

  8. Applied associate-*r*0.0

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

  9. Simplified0.0

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

  11. Applied add-cube-cbrt0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 
(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))))