Average Error: 16.5 → 0.0
Time: 34.4s
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 r431934 = x;
        double r431935 = 1.0;
        double r431936 = r431935 - r431934;
        double r431937 = y;
        double r431938 = r431935 - r431937;
        double r431939 = r431936 * r431938;
        double r431940 = r431934 + r431939;
        return r431940;
}
↓
double f(double x, double y) {
        double r431941 = 1.0;
        double r431942 = y;
        double r431943 = x;
        double r431944 = r431942 * r431943;
        double r431945 = -r431941;
        double r431946 = r431942 * r431945;
        double r431947 = r431944 + r431946;
        double r431948 = r431941 + r431947;
        return r431948;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.5
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 16.5

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

  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 2019323 
(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))))