Average Error: 16.3 → 0.0
Time: 7.2s
Precision: 64
\[x + \left(1 - x\right) \cdot \left(1 - y\right)\]
↓
\[1 + \left(x - 1\right) \cdot y\]
x + \left(1 - x\right) \cdot \left(1 - y\right)
↓
1 + \left(x - 1\right) \cdot y
double f(double x, double y) {
        double r30271759 = x;
        double r30271760 = 1.0;
        double r30271761 = r30271760 - r30271759;
        double r30271762 = y;
        double r30271763 = r30271760 - r30271762;
        double r30271764 = r30271761 * r30271763;
        double r30271765 = r30271759 + r30271764;
        return r30271765;
}
↓
double f(double x, double y) {
        double r30271766 = 1.0;
        double r30271767 = x;
        double r30271768 = r30271767 - r30271766;
        double r30271769 = y;
        double r30271770 = r30271768 * r30271769;
        double r30271771 = r30271766 + r30271770;
        return r30271771;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.3
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 16.3

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"

  :herbie-target
  (- (* y x) (- y 1.0))

  (+ x (* (- 1.0 x) (- 1.0 y))))