Average Error: 0.0 → 0
Time: 928.0ms
Precision: binary64
\[\left(x + y\right) + x\]
↓
\[\sqrt[3]{-1} \cdot \left(x \cdot -2 - y\right)\]
\left(x + y\right) + x
↓
\sqrt[3]{-1} \cdot \left(x \cdot -2 - y\right)
double code(double x, double y) {
	return ((double) (((double) (x + y)) + x));
}
↓
double code(double x, double y) {
	return ((double) (((double) cbrt(-1.0)) * ((double) (((double) (x * -2.0)) - y))));
}

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-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

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

  5. Taylor expanded around -inf 0

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

  6. Simplified0

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

  7. Final simplification0

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

Reproduce

herbie shell --seed 2020182 
(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))