Average Error: 0.0 → 0.0
Time: 8.4s
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 r522502 = x;
        double r522503 = y;
        double r522504 = r522503 * r522503;
        double r522505 = exp(r522504);
        double r522506 = r522502 * r522505;
        return r522506;
}
↓
double f(double x, double y) {
        double r522507 = y;
        double r522508 = exp(r522507);
        double r522509 = 2.0;
        double r522510 = r522507 / r522509;
        double r522511 = r522509 * r522510;
        double r522512 = pow(r522508, r522511);
        double r522513 = x;
        double r522514 = r522512 * r522513;
        return r522514;
}

Error

Bits error versus x

Bits error versus y

Try it out

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 2019291 
(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))))