Average Error: 0.0 → 0.0
Time: 17.8s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot {\left(e^{y}\right)}^{y}\]
x \cdot e^{y \cdot y}
↓
x \cdot {\left(e^{y}\right)}^{y}
double f(double x, double y) {
        double r1022216 = x;
        double r1022217 = y;
        double r1022218 = r1022217 * r1022217;
        double r1022219 = exp(r1022218);
        double r1022220 = r1022216 * r1022219;
        return r1022220;
}
↓
double f(double x, double y) {
        double r1022221 = x;
        double r1022222 = y;
        double r1022223 = exp(r1022222);
        double r1022224 = pow(r1022223, r1022222);
        double r1022225 = r1022221 * r1022224;
        return r1022225;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(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))))