Average Error: 0.1 → 0.1
Time: 55.7s
Precision: 64
\[x \cdot \left(y + z\right) + z \cdot 5\]
↓
\[z \cdot \left(5 + x\right) + y \cdot x\]
x \cdot \left(y + z\right) + z \cdot 5
↓
z \cdot \left(5 + x\right) + y \cdot x
double f(double x, double y, double z) {
        double r28167698 = x;
        double r28167699 = y;
        double r28167700 = z;
        double r28167701 = r28167699 + r28167700;
        double r28167702 = r28167698 * r28167701;
        double r28167703 = 5.0;
        double r28167704 = r28167700 * r28167703;
        double r28167705 = r28167702 + r28167704;
        return r28167705;
}
↓
double f(double x, double y, double z) {
        double r28167706 = z;
        double r28167707 = 5.0;
        double r28167708 = x;
        double r28167709 = r28167707 + r28167708;
        double r28167710 = r28167706 * r28167709;
        double r28167711 = y;
        double r28167712 = r28167711 * r28167708;
        double r28167713 = r28167710 + r28167712;
        return r28167713;
}

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. Using strategy rm

  7. Applied add-sqr-sqrt12.4

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

  8. Applied associate-*r*12.2

    \[\leadsto x \cdot y + \color{blue}{\left(z \cdot \sqrt{x + 5}\right) \cdot \sqrt{x + 5}}\]
  9. Using strategy rm

  10. Applied associate-*l*12.4

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(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)))