Average Error: 16.6 → 0.0
Time: 21.2s
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 r1238358 = x;
        double r1238359 = 1.0;
        double r1238360 = r1238359 - r1238358;
        double r1238361 = y;
        double r1238362 = r1238359 - r1238361;
        double r1238363 = r1238360 * r1238362;
        double r1238364 = r1238358 + r1238363;
        return r1238364;
}
↓
double f(double x, double y) {
        double r1238365 = x;
        double r1238366 = y;
        double r1238367 = r1238365 * r1238366;
        double r1238368 = 1.0;
        double r1238369 = -r1238368;
        double r1238370 = r1238369 * r1238366;
        double r1238371 = r1238367 + r1238370;
        double r1238372 = r1238371 + r1238368;
        return r1238372;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original16.6
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 16.6

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

  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 2020047 
(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))))