Average Error: 0.1 → 0.1
Time: 13.8s
Precision: 64
\[x \cdot \left(y + z\right) + z \cdot 5\]
↓
\[x \cdot y + z \cdot \left(x + 5\right)\]
x \cdot \left(y + z\right) + z \cdot 5
↓
x \cdot y + z \cdot \left(x + 5\right)
double f(double x, double y, double z) {
        double r341345 = x;
        double r341346 = y;
        double r341347 = z;
        double r341348 = r341346 + r341347;
        double r341349 = r341345 * r341348;
        double r341350 = 5.0;
        double r341351 = r341347 * r341350;
        double r341352 = r341349 + r341351;
        return r341352;
}
↓
double f(double x, double y, double z) {
        double r341353 = x;
        double r341354 = y;
        double r341355 = r341353 * r341354;
        double r341356 = z;
        double r341357 = 5.0;
        double r341358 = r341353 + r341357;
        double r341359 = r341356 * r341358;
        double r341360 = r341355 + r341359;
        return r341360;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(x + 5\right) \cdot z + x \cdot y\]

Derivation

  1. Initial program 0.1

    \[x \cdot \left(y + z\right) + z \cdot 5\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(x \cdot y + x \cdot z\right)} + z \cdot 5\]

  4. Applied associate-+l+0.1

    \[\leadsto \color{blue}{x \cdot y + \left(x \cdot z + z \cdot 5\right)}\]

  5. Simplified0.1

    \[\leadsto x \cdot y + \color{blue}{z \cdot \left(x + 5\right)}\]

  6. Final simplification0.1

    \[\leadsto x \cdot y + z \cdot \left(x + 5\right)\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5) z) (* x y))

  (+ (* x (+ y z)) (* z 5)))