Average Error: 0.1 → 0.1
Time: 3.4s
Precision: 64
\[x \cdot \left(y + z\right) + z \cdot 5\]
↓
\[x \cdot \left(y + z\right) + z \cdot 5\]
x \cdot \left(y + z\right) + z \cdot 5
↓
x \cdot \left(y + z\right) + z \cdot 5
double f(double x, double y, double z) {
        double r338024 = x;
        double r338025 = y;
        double r338026 = z;
        double r338027 = r338025 + r338026;
        double r338028 = r338024 * r338027;
        double r338029 = 5.0;
        double r338030 = r338026 * r338029;
        double r338031 = r338028 + r338030;
        return r338031;
}
↓
double f(double x, double y, double z) {
        double r338032 = x;
        double r338033 = y;
        double r338034 = z;
        double r338035 = r338033 + r338034;
        double r338036 = r338032 * r338035;
        double r338037 = 5.0;
        double r338038 = r338034 * r338037;
        double r338039 = r338036 + r338038;
        return r338039;
}

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-lft-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 1978988140 
(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)))