Average Error: 0.0 → 0
Time: 879.0ms
Precision: 64
\[\left(x + y\right) + x\]
↓
\[2 \cdot x + y\]
\left(x + y\right) + x
↓
2 \cdot x + y
double f(double x, double y) {
        double r509141 = x;
        double r509142 = y;
        double r509143 = r509141 + r509142;
        double r509144 = r509143 + r509141;
        return r509144;
}
↓
double f(double x, double y) {
        double r509145 = 2.0;
        double r509146 = x;
        double r509147 = r509145 * r509146;
        double r509148 = y;
        double r509149 = r509147 + r509148;
        return r509149;
}

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 flip-+47.0

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

  4. Simplified47.0

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

  5. Simplified23.7

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

  6. Taylor expanded around 0 0

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

  7. Final simplification0

    \[\leadsto 2 \cdot x + y\]

Reproduce

herbie shell --seed 2020034 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ y (* 2 x))

  (+ (+ x y) x))