Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\right) \cdot \sqrt{{\left(e^{y}\right)}^{y}}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\right) \cdot \sqrt{{\left(e^{y}\right)}^{y}}
double f(double x, double y) {
        double r857954 = x;
        double r857955 = y;
        double r857956 = r857955 * r857955;
        double r857957 = exp(r857956);
        double r857958 = r857954 * r857957;
        return r857958;
}
↓
double f(double x, double y) {
        double r857959 = x;
        double r857960 = y;
        double r857961 = exp(r857960);
        double r857962 = 2.0;
        double r857963 = r857960 / r857962;
        double r857964 = pow(r857961, r857963);
        double r857965 = r857959 * r857964;
        double r857966 = pow(r857961, r857960);
        double r857967 = sqrt(r857966);
        double r857968 = r857965 * r857967;
        return r857968;
}

Error

Bits error versus x

Bits error versus y

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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

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

  7. Applied associate-*r*0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 
(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))))