Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\sqrt{e^{y \cdot y}} \cdot \left({\left(e^{y}\right)}^{\left(\frac{y}{2}\right)} \cdot x\right)\]
x \cdot e^{y \cdot y}
↓
\sqrt{e^{y \cdot y}} \cdot \left({\left(e^{y}\right)}^{\left(\frac{y}{2}\right)} \cdot x\right)
double f(double x, double y) {
        double r40221296 = x;
        double r40221297 = y;
        double r40221298 = r40221297 * r40221297;
        double r40221299 = exp(r40221298);
        double r40221300 = r40221296 * r40221299;
        return r40221300;
}
↓
double f(double x, double y) {
        double r40221301 = y;
        double r40221302 = r40221301 * r40221301;
        double r40221303 = exp(r40221302);
        double r40221304 = sqrt(r40221303);
        double r40221305 = exp(r40221301);
        double r40221306 = 2.0;
        double r40221307 = r40221301 / r40221306;
        double r40221308 = pow(r40221305, r40221307);
        double r40221309 = x;
        double r40221310 = r40221308 * r40221309;
        double r40221311 = r40221304 * r40221310;
        return r40221311;
}

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-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

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

  6. Applied add-log-exp0.0

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

  7. Applied exp-to-pow0.0

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

  8. Applied sqrt-pow10.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(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))))