Average Error: 0.0 → 0
Time: 1.7s
Precision: binary64
\[\left(x + y\right) + x\]
↓
\[-2 \cdot \left(\sqrt[3]{-1} \cdot x\right) - \sqrt[3]{-1} \cdot y\]
\left(x + y\right) + x
↓
-2 \cdot \left(\sqrt[3]{-1} \cdot x\right) - \sqrt[3]{-1} \cdot y
double code(double x, double y) {
	return ((double) (((double) (x + y)) + x));
}
↓
double code(double x, double y) {
	return ((double) (((double) (-2.0 * ((double) (((double) cbrt(-1.0)) * x)))) - ((double) (((double) cbrt(-1.0)) * y))));
}

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-cube42.5

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

  4. Simplified42.5

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

  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. Simplified0

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

  7. Final simplification0

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

Reproduce

herbie shell --seed 2020150 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"
  :precision binary64

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

  (+ (+ x y) x))