Average Error: 16.2 → 0.0
Time: 1.2s
Precision: 64
\[x + \left(1 - x\right) \cdot \left(1 - y\right)\]
↓
\[y \cdot \left(x - 1\right) + 1\]
x + \left(1 - x\right) \cdot \left(1 - y\right)
↓
y \cdot \left(x - 1\right) + 1
double f(double x, double y) {
        double r539437 = x;
        double r539438 = 1.0;
        double r539439 = r539438 - r539437;
        double r539440 = y;
        double r539441 = r539438 - r539440;
        double r539442 = r539439 * r539441;
        double r539443 = r539437 + r539442;
        return r539443;
}
↓
double f(double x, double y) {
        double r539444 = y;
        double r539445 = x;
        double r539446 = 1.0;
        double r539447 = r539445 - r539446;
        double r539448 = r539444 * r539447;
        double r539449 = r539448 + r539446;
        return r539449;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.2
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 16.2

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

  2. Taylor expanded around 0 0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 
(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))))