Average Error: 0.0 → 0
Time: 889.0ms
Precision: 64
\[\left(x + y\right) + x\]
↓
\[-\left(2 \cdot \left(\sqrt[3]{-1} \cdot x\right) + \sqrt[3]{-1} \cdot y\right)\]
\left(x + y\right) + x
↓
-\left(2 \cdot \left(\sqrt[3]{-1} \cdot x\right) + \sqrt[3]{-1} \cdot y\right)
double f(double x, double y) {
        double r706441 = x;
        double r706442 = y;
        double r706443 = r706441 + r706442;
        double r706444 = r706443 + r706441;
        return r706444;
}
↓
double f(double x, double y) {
        double r706445 = 2.0;
        double r706446 = -1.0;
        double r706447 = cbrt(r706446);
        double r706448 = x;
        double r706449 = r706447 * r706448;
        double r706450 = r706445 * r706449;
        double r706451 = y;
        double r706452 = r706447 * r706451;
        double r706453 = r706450 + r706452;
        double r706454 = -r706453;
        return r706454;
}

Error

Bits error versus x

Bits error versus y

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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-cbrt-cube42.4

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\left(x + y\right) + x\right) \cdot \left(\left(x + y\right) + x\right)\right) \cdot \left(\left(x + y\right) + x\right)}}\]

  4. Simplified42.4

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\left(x + y\right) + x\right)}^{3}}}\]

  5. Taylor expanded around -inf 0

    \[\leadsto \color{blue}{-\left(2 \cdot \left(\sqrt[3]{-1} \cdot x\right) + \sqrt[3]{-1} \cdot y\right)}\]

  6. Final simplification0

    \[\leadsto -\left(2 \cdot \left(\sqrt[3]{-1} \cdot x\right) + \sqrt[3]{-1} \cdot y\right)\]

Reproduce

herbie shell --seed 2019362 
(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))