Average Error: 0.1 → 0.1
Time: 10.2s
Precision: 64
\[x \cdot \left(y + z\right) + z \cdot 5\]
↓
\[x \cdot \left(y + z\right) + 5 \cdot z\]
x \cdot \left(y + z\right) + z \cdot 5
↓
x \cdot \left(y + z\right) + 5 \cdot z
double f(double x, double y, double z) {
        double r464037 = x;
        double r464038 = y;
        double r464039 = z;
        double r464040 = r464038 + r464039;
        double r464041 = r464037 * r464040;
        double r464042 = 5.0;
        double r464043 = r464039 * r464042;
        double r464044 = r464041 + r464043;
        return r464044;
}
↓
double f(double x, double y, double z) {
        double r464045 = x;
        double r464046 = y;
        double r464047 = z;
        double r464048 = r464046 + r464047;
        double r464049 = r464045 * r464048;
        double r464050 = 5.0;
        double r464051 = r464050 * r464047;
        double r464052 = r464049 + r464051;
        return r464052;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

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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. Using strategy rm

  7. Applied distribute-rgt-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019294 
(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)))