Average Error: 0.0 → 0
Time: 1.1s
Precision: 64
\[\left(x + y\right) + x\]
↓
\[2 \cdot x + y\]
\left(x + y\right) + x
↓
2 \cdot x + y
double f(double x, double y) {
        double r762453 = x;
        double r762454 = y;
        double r762455 = r762453 + r762454;
        double r762456 = r762455 + r762453;
        return r762456;
}
↓
double f(double x, double y) {
        double r762457 = 2.0;
        double r762458 = x;
        double r762459 = r762457 * r762458;
        double r762460 = y;
        double r762461 = r762459 + r762460;
        return r762461;
}

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 flip3-+42.1

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

  4. Simplified42.1

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

  5. Taylor expanded around 0 0

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

  6. Final simplification0

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

Reproduce

herbie shell --seed 2020057 
(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))