Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[{\left(e^{y}\right)}^{\left(2 \cdot \frac{y}{2}\right)} \cdot x\]
x \cdot e^{y \cdot y}
↓
{\left(e^{y}\right)}^{\left(2 \cdot \frac{y}{2}\right)} \cdot x
double f(double x, double y) {
        double r581345 = x;
        double r581346 = y;
        double r581347 = r581346 * r581346;
        double r581348 = exp(r581347);
        double r581349 = r581345 * r581348;
        return r581349;
}
↓
double f(double x, double y) {
        double r581350 = y;
        double r581351 = exp(r581350);
        double r581352 = 2.0;
        double r581353 = r581350 / r581352;
        double r581354 = r581352 * r581353;
        double r581355 = pow(r581351, r581354);
        double r581356 = x;
        double r581357 = r581355 * r581356;
        return r581357;
}

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 sqr-pow0.0

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

  7. Applied associate-*r*0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019297 
(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))))