Average Error: 16.5 → 0.0
Time: 1.4s
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 r569580 = x;
        double r569581 = 1.0;
        double r569582 = r569581 - r569580;
        double r569583 = y;
        double r569584 = r569581 - r569583;
        double r569585 = r569582 * r569584;
        double r569586 = r569580 + r569585;
        return r569586;
}
↓
double f(double x, double y) {
        double r569587 = y;
        double r569588 = x;
        double r569589 = 1.0;
        double r569590 = r569588 - r569589;
        double r569591 = r569587 * r569590;
        double r569592 = r569591 + r569589;
        return r569592;
}

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. 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 2020081 
(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))))