Average Error: 0.0 → 0.0
Time: 14.1s
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 r39727355 = x;
        double r39727356 = y;
        double r39727357 = r39727356 * r39727356;
        double r39727358 = exp(r39727357);
        double r39727359 = r39727355 * r39727358;
        return r39727359;
}
↓
double f(double x, double y) {
        double r39727360 = y;
        double r39727361 = exp(r39727360);
        double r39727362 = pow(r39727361, r39727360);
        double r39727363 = x;
        double r39727364 = r39727362 * r39727363;
        return r39727364;
}

Error

Bits error versus x

Bits error versus y

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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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(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))))