Average Error: 0.0 → 0.1
Time: 15.7s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\sqrt{\sqrt[3]{e^{y \cdot y}}} \cdot \left(\sqrt{e^{y \cdot y}} \cdot \left(\left|\sqrt[3]{e^{y \cdot y}}\right| \cdot x\right)\right)\]
x \cdot e^{y \cdot y}
↓
\sqrt{\sqrt[3]{e^{y \cdot y}}} \cdot \left(\sqrt{e^{y \cdot y}} \cdot \left(\left|\sqrt[3]{e^{y \cdot y}}\right| \cdot x\right)\right)
double f(double x, double y) {
        double r37491989 = x;
        double r37491990 = y;
        double r37491991 = r37491990 * r37491990;
        double r37491992 = exp(r37491991);
        double r37491993 = r37491989 * r37491992;
        return r37491993;
}
↓
double f(double x, double y) {
        double r37491994 = y;
        double r37491995 = r37491994 * r37491994;
        double r37491996 = exp(r37491995);
        double r37491997 = cbrt(r37491996);
        double r37491998 = sqrt(r37491997);
        double r37491999 = sqrt(r37491996);
        double r37492000 = fabs(r37491997);
        double r37492001 = x;
        double r37492002 = r37492000 * r37492001;
        double r37492003 = r37491999 * r37492002;
        double r37492004 = r37491998 * r37492003;
        return r37492004;
}

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-cbrt0.1

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

  7. Applied sqrt-prod0.1

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

  8. Applied associate-*r*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 +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))))