Average Error: 0.0 → 0.1
Time: 4.6s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}} \cdot \sqrt[3]{e^{y \cdot y}}} \cdot {\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right)}^{4}\right)\right) \cdot \sqrt[3]{e^{y \cdot y}}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}} \cdot \sqrt[3]{e^{y \cdot y}}} \cdot {\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right)}^{4}\right)\right) \cdot \sqrt[3]{e^{y \cdot y}}
double f(double x, double y) {
        double r926157 = x;
        double r926158 = y;
        double r926159 = r926158 * r926158;
        double r926160 = exp(r926159);
        double r926161 = r926157 * r926160;
        return r926161;
}
↓
double f(double x, double y) {
        double r926162 = x;
        double r926163 = y;
        double r926164 = r926163 * r926163;
        double r926165 = exp(r926164);
        double r926166 = cbrt(r926165);
        double r926167 = r926166 * r926166;
        double r926168 = cbrt(r926167);
        double r926169 = cbrt(r926166);
        double r926170 = 4.0;
        double r926171 = pow(r926169, r926170);
        double r926172 = r926168 * r926171;
        double r926173 = r926162 * r926172;
        double r926174 = r926173 * r926166;
        return r926174;
}

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-cube-cbrt0.0

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

  4. Applied associate-*r*0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied cbrt-prod0.0

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

  8. Applied associate-*l*0.0

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

  9. Simplified0.1

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}} \cdot \sqrt[3]{e^{y \cdot y}}} \cdot \color{blue}{{\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right)}^{4}}\right)\right) \cdot \sqrt[3]{e^{y \cdot y}}\]

  10. Final simplification0.1

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}} \cdot \sqrt[3]{e^{y \cdot y}}} \cdot {\left(\sqrt[3]{\sqrt[3]{e^{y \cdot y}}}\right)}^{4}\right)\right) \cdot \sqrt[3]{e^{y \cdot y}}\]

Reproduce

herbie shell --seed 2020025 
(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))))