Average Error: 0.0 → 0.0
Time: 18.4s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot \left(\left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right) \cdot \left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right)\right)\]
x \cdot e^{y \cdot y}
↓
x \cdot \left(\left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right) \cdot \left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right)\right)
double f(double x, double y) {
        double r867795 = x;
        double r867796 = y;
        double r867797 = r867796 * r867796;
        double r867798 = exp(r867797);
        double r867799 = r867795 * r867798;
        return r867799;
}
↓
double f(double x, double y) {
        double r867800 = x;
        double r867801 = y;
        double r867802 = exp(r867801);
        double r867803 = sqrt(r867802);
        double r867804 = sqrt(r867803);
        double r867805 = pow(r867804, r867801);
        double r867806 = pow(r867803, r867801);
        double r867807 = sqrt(r867806);
        double r867808 = r867805 * r867807;
        double r867809 = r867808 * r867808;
        double r867810 = r867800 * r867809;
        return r867810;
}

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 add-sqr-sqrt0.0

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

  7. Applied unpow-prod-down0.0

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

  9. Applied add-sqr-sqrt0.0

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

  10. Applied add-sqr-sqrt0.0

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

  11. Applied sqrt-prod0.0

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

  12. Applied unpow-prod-down0.0

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

  13. Applied unswap-sqr0.0

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

  14. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +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))))