Average Error: 16.3 → 0.0
Time: 25.5s
Precision: 64
\[x + \left(1 - x\right) \cdot \left(1 - y\right)\]
↓
\[\left(x \cdot y + \left(-1\right) \cdot y\right) + 1\]
x + \left(1 - x\right) \cdot \left(1 - y\right)
↓
\left(x \cdot y + \left(-1\right) \cdot y\right) + 1
double f(double x, double y) {
        double r519263 = x;
        double r519264 = 1.0;
        double r519265 = r519264 - r519263;
        double r519266 = y;
        double r519267 = r519264 - r519266;
        double r519268 = r519265 * r519267;
        double r519269 = r519263 + r519268;
        return r519269;
}
↓
double f(double x, double y) {
        double r519270 = x;
        double r519271 = y;
        double r519272 = r519270 * r519271;
        double r519273 = 1.0;
        double r519274 = -r519273;
        double r519275 = r519274 * r519271;
        double r519276 = r519272 + r519275;
        double r519277 = r519276 + r519273;
        return r519277;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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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

    \[\leadsto \color{blue}{y \cdot \left(x - 1\right) + 1}\]
  4. Using strategy rm

  5. Applied sub-neg0.0

    \[\leadsto y \cdot \color{blue}{\left(x + \left(-1\right)\right)} + 1\]

  6. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(y \cdot x + y \cdot \left(-1\right)\right)} + 1\]

  7. Simplified0.0

    \[\leadsto \left(\color{blue}{x \cdot y} + y \cdot \left(-1\right)\right) + 1\]

  8. Simplified0.0

    \[\leadsto \left(x \cdot y + \color{blue}{\left(-1\right) \cdot y}\right) + 1\]

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(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))))