Average Error: 0.0 → 0
Time: 4.7s
Precision: 64
\[\left(x + y\right) + x\]
↓
\[\left(x + x\right) + y\]
\left(x + y\right) + x
↓
\left(x + x\right) + y
double f(double x, double y) {
        double r504905 = x;
        double r504906 = y;
        double r504907 = r504905 + r504906;
        double r504908 = r504907 + r504905;
        return r504908;
}
↓
double f(double x, double y) {
        double r504909 = x;
        double r504910 = r504909 + r504909;
        double r504911 = y;
        double r504912 = r504910 + r504911;
        return r504912;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0
Herbie0
\[y + 2 \cdot x\]

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) + x\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt32.0

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

  4. Simplified32.0

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

  5. Simplified32.0

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

  7. Applied associate-+r+32.0

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

  8. Simplified32.0

    \[\leadsto \sqrt{\color{blue}{2 \cdot x} + y} \cdot \sqrt{x + \left(x + y\right)}\]

  9. Taylor expanded around 0 0

    \[\leadsto \color{blue}{2 \cdot x + y}\]

  10. Simplified0

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

  11. Final simplification0

    \[\leadsto \left(x + x\right) + y\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"

  :herbie-target
  (+ y (* 2.0 x))

  (+ (+ x y) x))