Average Error: 16.0 → 0.0
Time: 7.9s
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 r581521 = x;
        double r581522 = 1.0;
        double r581523 = r581522 - r581521;
        double r581524 = y;
        double r581525 = r581522 - r581524;
        double r581526 = r581523 * r581525;
        double r581527 = r581521 + r581526;
        return r581527;
}
↓
double f(double x, double y) {
        double r581528 = 1.0;
        double r581529 = y;
        double r581530 = x;
        double r581531 = r581530 - r581528;
        double r581532 = r581529 * r581531;
        double r581533 = r581528 + r581532;
        return r581533;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 16.0

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Taylor expanded around 0 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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))))