Average Error: 0.0 → 0.0
Time: 14.9s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[{e}^{\left({y}^{2}\right)} \cdot x\]
x \cdot e^{y \cdot y}
↓
{e}^{\left({y}^{2}\right)} \cdot x
double f(double x, double y) {
        double r554855 = x;
        double r554856 = y;
        double r554857 = r554856 * r554856;
        double r554858 = exp(r554857);
        double r554859 = r554855 * r554858;
        return r554859;
}
↓
double f(double x, double y) {
        double r554860 = exp(1.0);
        double r554861 = y;
        double r554862 = 2.0;
        double r554863 = pow(r554861, r554862);
        double r554864 = pow(r554860, r554863);
        double r554865 = x;
        double r554866 = r554864 * r554865;
        return r554866;
}

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 *-un-lft-identity0.0

    \[\leadsto x \cdot {\left(e^{\color{blue}{1 \cdot y}}\right)}^{y}\]

  7. Applied exp-prod0.0

    \[\leadsto x \cdot {\color{blue}{\left({\left(e^{1}\right)}^{y}\right)}}^{y}\]

  8. Applied pow-pow0.0

    \[\leadsto x \cdot \color{blue}{{\left(e^{1}\right)}^{\left(y \cdot y\right)}}\]

  9. Simplified0.0

    \[\leadsto x \cdot {\left(e^{1}\right)}^{\color{blue}{\left({y}^{2}\right)}}\]

  10. Final simplification0.0

    \[\leadsto {e}^{\left({y}^{2}\right)} \cdot x\]

Reproduce

herbie shell --seed 2019198 +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))))