Average Error: 0.1 → 0.1
Time: 2.7s
Precision: 64
\[x \cdot \left(y + z\right) + z \cdot 5\]
↓
\[y \cdot x + z \cdot \left(x + 5\right)\]
x \cdot \left(y + z\right) + z \cdot 5
↓
y \cdot x + z \cdot \left(x + 5\right)
double f(double x, double y, double z) {
        double r1361848 = x;
        double r1361849 = y;
        double r1361850 = z;
        double r1361851 = r1361849 + r1361850;
        double r1361852 = r1361848 * r1361851;
        double r1361853 = 5.0;
        double r1361854 = r1361850 * r1361853;
        double r1361855 = r1361852 + r1361854;
        return r1361855;
}
↓
double f(double x, double y, double z) {
        double r1361856 = y;
        double r1361857 = x;
        double r1361858 = r1361856 * r1361857;
        double r1361859 = z;
        double r1361860 = 5.0;
        double r1361861 = r1361857 + r1361860;
        double r1361862 = r1361859 * r1361861;
        double r1361863 = r1361858 + r1361862;
        return r1361863;
}

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-rgt-in0.1

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

  4. Applied associate-+l+0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 
(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)))