Average Error: 0.0 → 0
Time: 9.8s
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 r386565 = x;
        double r386566 = y;
        double r386567 = r386565 + r386566;
        double r386568 = r386567 + r386565;
        return r386568;
}
↓
double f(double x, double y) {
        double r386569 = 2.0;
        double r386570 = x;
        double r386571 = r386569 * r386570;
        double r386572 = y;
        double r386573 = r386571 + r386572;
        return r386573;
}

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-sqr-sqrt32.7

    \[\leadsto \color{blue}{\sqrt{\left(x + y\right) + x} \cdot \sqrt{\left(x + y\right) + x}}\]
  4. Using strategy rm

  5. Applied flip-+55.7

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

  6. Applied sqrt-div55.8

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

  7. Applied flip-+55.8

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

  8. Applied sqrt-div55.9

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

  9. Applied frac-times55.9

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

  10. Simplified55.7

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

  11. Simplified47.5

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

  12. Taylor expanded around 0 0

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

  13. Final simplification0

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

Reproduce

herbie shell --seed 2019303 
(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))