Average Error: 16.3 → 0.0
Time: 1.1s
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 r547001 = x;
        double r547002 = 1.0;
        double r547003 = r547002 - r547001;
        double r547004 = y;
        double r547005 = r547002 - r547004;
        double r547006 = r547003 * r547005;
        double r547007 = r547001 + r547006;
        return r547007;
}
↓
double f(double x, double y) {
        double r547008 = y;
        double r547009 = x;
        double r547010 = 1.0;
        double r547011 = r547009 - r547010;
        double r547012 = r547008 * r547011;
        double r547013 = r547012 + r547010;
        return r547013;
}

Error

Bits error versus x

Bits error versus y

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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. 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 2020062 
(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))))