Average Error: 0.0 → 0.0
Time: 15.8s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[{\left(e^{y}\right)}^{y} \cdot x\]
x \cdot e^{y \cdot y}
↓
{\left(e^{y}\right)}^{y} \cdot x
double f(double x, double y) {
        double r631877 = x;
        double r631878 = y;
        double r631879 = r631878 * r631878;
        double r631880 = exp(r631879);
        double r631881 = r631877 * r631880;
        return r631881;
}
↓
double f(double x, double y) {
        double r631882 = y;
        double r631883 = exp(r631882);
        double r631884 = pow(r631883, r631882);
        double r631885 = x;
        double r631886 = r631884 * r631885;
        return r631886;
}

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. Simplified0.0

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied associate-*l*0.0

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

  7. Applied *-un-lft-identity0.0

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

  8. Applied associate-*l*0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(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))))