Average Error: 16.1 → 0.0
Time: 10.1s
Precision: 64
\[x + \left(1.0 - x\right) \cdot \left(1.0 - y\right)\]
↓
\[1.0 + \left(x - 1.0\right) \cdot y\]
x + \left(1.0 - x\right) \cdot \left(1.0 - y\right)
↓
1.0 + \left(x - 1.0\right) \cdot y
double f(double x, double y) {
        double r29788255 = x;
        double r29788256 = 1.0;
        double r29788257 = r29788256 - r29788255;
        double r29788258 = y;
        double r29788259 = r29788256 - r29788258;
        double r29788260 = r29788257 * r29788259;
        double r29788261 = r29788255 + r29788260;
        return r29788261;
}
↓
double f(double x, double y) {
        double r29788262 = 1.0;
        double r29788263 = x;
        double r29788264 = r29788263 - r29788262;
        double r29788265 = y;
        double r29788266 = r29788264 * r29788265;
        double r29788267 = r29788262 + r29788266;
        return r29788267;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.1
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1.0\right)\]

Derivation

  1. Initial program 16.1

    \[x + \left(1.0 - x\right) \cdot \left(1.0 - y\right)\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(1.0 + x \cdot y\right) - 1.0 \cdot y}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - 1.0\right) + 1.0}\]

  4. Final simplification0.0

    \[\leadsto 1.0 + \left(x - 1.0\right) \cdot y\]

Reproduce

herbie shell --seed 2019163 
(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))))