Average Error: 0.0 → 0.0
Time: 21.1s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \sqrt{e^{y \cdot y}}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \sqrt{e^{y \cdot y}}
double f(double x, double y) {
        double r568160 = x;
        double r568161 = y;
        double r568162 = r568161 * r568161;
        double r568163 = exp(r568162);
        double r568164 = r568160 * r568163;
        return r568164;
}
↓
double f(double x, double y) {
        double r568165 = x;
        double r568166 = y;
        double r568167 = r568166 * r568166;
        double r568168 = exp(r568167);
        double r568169 = sqrt(r568168);
        double r568170 = r568165 * r568169;
        double r568171 = r568170 * r568169;
        return r568171;
}

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-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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019347 +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))))