Average Error: 16.0 → 0.0
Time: 11.8s
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 r750822 = x;
        double r750823 = 1.0;
        double r750824 = r750823 - r750822;
        double r750825 = y;
        double r750826 = r750823 - r750825;
        double r750827 = r750824 * r750826;
        double r750828 = r750822 + r750827;
        return r750828;
}
↓
double f(double x, double y) {
        double r750829 = 1.0;
        double r750830 = y;
        double r750831 = x;
        double r750832 = r750831 - r750829;
        double r750833 = r750830 * r750832;
        double r750834 = r750829 + r750833;
        return r750834;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 16.0

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

  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 2020045 +o rules:numerics
(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))))