Average Error: 0.1 → 0.1
Time: 11.4s
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 r28255436 = x;
        double r28255437 = y;
        double r28255438 = z;
        double r28255439 = r28255437 + r28255438;
        double r28255440 = r28255436 * r28255439;
        double r28255441 = 5.0;
        double r28255442 = r28255438 * r28255441;
        double r28255443 = r28255440 + r28255442;
        return r28255443;
}
↓
double f(double x, double y, double z) {
        double r28255444 = x;
        double r28255445 = y;
        double r28255446 = r28255444 * r28255445;
        double r28255447 = z;
        double r28255448 = 5.0;
        double r28255449 = r28255444 + r28255448;
        double r28255450 = r28255447 * r28255449;
        double r28255451 = r28255446 + r28255450;
        return r28255451;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))