Average Error: 16.6 → 0.0
Time: 19.6s
Precision: 64
\[x + \left(1 - x\right) \cdot \left(1 - y\right)\]
↓
\[1 + y \cdot \left(x - 1\right)\]
x + \left(1 - x\right) \cdot \left(1 - y\right)
↓
1 + y \cdot \left(x - 1\right)
double f(double x, double y) {
        double r626289 = x;
        double r626290 = 1.0;
        double r626291 = r626290 - r626289;
        double r626292 = y;
        double r626293 = r626290 - r626292;
        double r626294 = r626291 * r626293;
        double r626295 = r626289 + r626294;
        return r626295;
}
↓
double f(double x, double y) {
        double r626296 = 1.0;
        double r626297 = y;
        double r626298 = x;
        double r626299 = r626298 - r626296;
        double r626300 = r626297 * r626299;
        double r626301 = r626296 + r626300;
        return r626301;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.6
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 16.6

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

  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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 
(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))))