Average Error: 15.8 → 0.0
Time: 1.8s
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 r587414 = x;
        double r587415 = 1.0;
        double r587416 = r587415 - r587414;
        double r587417 = y;
        double r587418 = r587415 - r587417;
        double r587419 = r587416 * r587418;
        double r587420 = r587414 + r587419;
        return r587420;
}
↓
double f(double x, double y) {
        double r587421 = y;
        double r587422 = x;
        double r587423 = 1.0;
        double r587424 = r587422 - r587423;
        double r587425 = r587421 * r587424;
        double r587426 = r587425 + r587423;
        return r587426;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.8
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 15.8

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

  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 2019354 
(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))))