Average Error: 0.0 → 0
Time: 10.6s
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 r325595 = x;
        double r325596 = y;
        double r325597 = r325595 + r325596;
        double r325598 = r325597 + r325595;
        return r325598;
}
↓
double f(double x, double y) {
        double r325599 = 2.0;
        double r325600 = x;
        double r325601 = r325599 * r325600;
        double r325602 = y;
        double r325603 = r325601 + r325602;
        return r325603;
}

Error

Bits error versus x

Bits error versus y

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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-sqrt32.5

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

  5. Applied add-sqr-sqrt32.5

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

  6. Simplified32.5

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

  7. Simplified32.5

    \[\leadsto \sqrt{2 \cdot x + y} \cdot \color{blue}{\sqrt{2 \cdot x + y}}\]
  8. Using strategy rm

  9. Applied pow1/232.5

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

  10. Applied pow1/232.5

    \[\leadsto \color{blue}{{\left(2 \cdot x + y\right)}^{\frac{1}{2}}} \cdot {\left(2 \cdot x + y\right)}^{\frac{1}{2}}\]

  11. Applied pow-prod-up0

    \[\leadsto \color{blue}{{\left(2 \cdot x + y\right)}^{\left(\frac{1}{2} + \frac{1}{2}\right)}}\]

  12. Simplified0

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

  13. Final simplification0

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

Reproduce

herbie shell --seed 2019326 
(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))