Average Error: 16.4 → 0.0
Time: 31.6s
Precision: 64
\[x + \left(1 - x\right) \cdot \left(1 - y\right)\]
↓
\[1 + \left(y \cdot x + y \cdot \left(-1\right)\right)\]
x + \left(1 - x\right) \cdot \left(1 - y\right)
↓
1 + \left(y \cdot x + y \cdot \left(-1\right)\right)
double f(double x, double y) {
        double r414903 = x;
        double r414904 = 1.0;
        double r414905 = r414904 - r414903;
        double r414906 = y;
        double r414907 = r414904 - r414906;
        double r414908 = r414905 * r414907;
        double r414909 = r414903 + r414908;
        return r414909;
}
↓
double f(double x, double y) {
        double r414910 = 1.0;
        double r414911 = y;
        double r414912 = x;
        double r414913 = r414911 * r414912;
        double r414914 = -r414910;
        double r414915 = r414911 * r414914;
        double r414916 = r414913 + r414915;
        double r414917 = r414910 + r414916;
        return r414917;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.4
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 16.4

    \[x + \left(1 - x\right) \cdot \left(1 - y\right)\]

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

    \[\leadsto \color{blue}{1 + y \cdot \left(x - 1\right)}\]
  4. Using strategy rm

  5. Applied sub-neg0.0

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

  6. Applied distribute-lft-in0.0

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

  7. Final simplification0.0

    \[\leadsto 1 + \left(y \cdot x + y \cdot \left(-1\right)\right)\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* y x) (- y 1))

  (+ x (* (- 1 x) (- 1 y))))