Average Error: 0.0 → 0
Time: 10.6s
Precision: 64
\[\left(x + y\right) + x\]
↓
\[y + 2 \cdot x\]
\left(x + y\right) + x
↓
y + 2 \cdot x
double f(double x, double y) {
        double r29681415 = x;
        double r29681416 = y;
        double r29681417 = r29681415 + r29681416;
        double r29681418 = r29681417 + r29681415;
        return r29681418;
}
↓
double f(double x, double y) {
        double r29681419 = y;
        double r29681420 = 2.0;
        double r29681421 = x;
        double r29681422 = r29681420 * r29681421;
        double r29681423 = r29681419 + r29681422;
        return r29681423;
}

Error

Bits error versus x

Bits error versus y

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Results

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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-sqrt31.8

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

  4. Taylor expanded around 0 0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2019171 
(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))