Average Error: 0.0 → 0
Time: 848.0ms
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 r645760 = x;
        double r645761 = y;
        double r645762 = r645760 + r645761;
        double r645763 = r645762 + r645760;
        return r645763;
}
↓
double f(double x, double y) {
        double r645764 = 2.0;
        double r645765 = -1.0;
        double r645766 = cbrt(r645765);
        double r645767 = x;
        double r645768 = r645766 * r645767;
        double r645769 = r645764 * r645768;
        double r645770 = y;
        double r645771 = r645766 * r645770;
        double r645772 = r645769 + r645771;
        double r645773 = -r645772;
        return r645773;
}

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-cbrt-cube41.6

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

  4. Simplified41.6

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

  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 2020027 
(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))