Average Error: 16.3 → 0.0
Time: 6.5s
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 r1672947 = x;
        double r1672948 = 1.0;
        double r1672949 = r1672948 - r1672947;
        double r1672950 = y;
        double r1672951 = r1672948 - r1672950;
        double r1672952 = r1672949 * r1672951;
        double r1672953 = r1672947 + r1672952;
        return r1672953;
}
↓
double f(double x, double y) {
        double r1672954 = 1.0;
        double r1672955 = y;
        double r1672956 = x;
        double r1672957 = r1672956 - r1672954;
        double r1672958 = r1672955 * r1672957;
        double r1672959 = r1672954 + r1672958;
        return r1672959;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.3
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 16.3

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

  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 2019235 
(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))))