Average Error: 16.2 → 0.0
Time: 13.4s
Precision: 64
\[x + \left(1 - x\right) \cdot \left(1 - y\right)\]
↓
\[1 + \left(x \cdot y + y \cdot \left(-1\right)\right)\]
x + \left(1 - x\right) \cdot \left(1 - y\right)
↓
1 + \left(x \cdot y + y \cdot \left(-1\right)\right)
double f(double x, double y) {
        double r27436190 = x;
        double r27436191 = 1.0;
        double r27436192 = r27436191 - r27436190;
        double r27436193 = y;
        double r27436194 = r27436191 - r27436193;
        double r27436195 = r27436192 * r27436194;
        double r27436196 = r27436190 + r27436195;
        return r27436196;
}
↓
double f(double x, double y) {
        double r27436197 = 1.0;
        double r27436198 = x;
        double r27436199 = y;
        double r27436200 = r27436198 * r27436199;
        double r27436201 = -r27436197;
        double r27436202 = r27436199 * r27436201;
        double r27436203 = r27436200 + r27436202;
        double r27436204 = r27436197 + r27436203;
        return r27436204;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.2
Target0.0
Herbie0.0
\[y \cdot x - \left(y - 1\right)\]

Derivation

  1. Initial program 16.2

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  5. Applied sub-neg0.0

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

  6. Applied distribute-lft-in0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"

  :herbie-target
  (- (* y x) (- y 1.0))

  (+ x (* (- 1.0 x) (- 1.0 y))))