Average Error: 0.1 → 0.1
Time: 13.4s
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 r371296 = x;
        double r371297 = y;
        double r371298 = z;
        double r371299 = r371297 + r371298;
        double r371300 = r371296 * r371299;
        double r371301 = 5.0;
        double r371302 = r371298 * r371301;
        double r371303 = r371300 + r371302;
        return r371303;
}
↓
double f(double x, double y, double z) {
        double r371304 = y;
        double r371305 = x;
        double r371306 = r371304 * r371305;
        double r371307 = z;
        double r371308 = 5.0;
        double r371309 = r371305 + r371308;
        double r371310 = r371307 * r371309;
        double r371311 = r371306 + r371310;
        return r371311;
}

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-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. Using strategy rm

  7. Applied flip3-+12.3

    \[\leadsto y \cdot x + z \cdot \color{blue}{\frac{{x}^{3} + {5}^{3}}{x \cdot x + \left(5 \cdot 5 - x \cdot 5\right)}}\]

  8. Applied associate-*r/14.6

    \[\leadsto y \cdot x + \color{blue}{\frac{z \cdot \left({x}^{3} + {5}^{3}\right)}{x \cdot x + \left(5 \cdot 5 - x \cdot 5\right)}}\]

  9. Taylor expanded around inf 0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(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)))