Average Error: 0.0 → 0.0
Time: 14.5s
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 r650209 = x;
        double r650210 = y;
        double r650211 = r650210 * r650210;
        double r650212 = exp(r650211);
        double r650213 = r650209 * r650212;
        return r650213;
}
↓
double f(double x, double y) {
        double r650214 = exp(1.0);
        double r650215 = y;
        double r650216 = 2.0;
        double r650217 = pow(r650215, r650216);
        double r650218 = pow(r650214, r650217);
        double r650219 = x;
        double r650220 = r650218 * r650219;
        return r650220;
}

Error

Bits error versus x

Bits error versus y

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Results

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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 
(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))))