Average Error: 0.0 → 0.0
Time: 10.7s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[y \cdot \left(x - z\right) + 1 \cdot z\]
x \cdot y + z \cdot \left(1 - y\right)
↓
y \cdot \left(x - z\right) + 1 \cdot z
double f(double x, double y, double z) {
        double r65317 = x;
        double r65318 = y;
        double r65319 = r65317 * r65318;
        double r65320 = z;
        double r65321 = 1.0;
        double r65322 = r65321 - r65318;
        double r65323 = r65320 * r65322;
        double r65324 = r65319 + r65323;
        return r65324;
}
↓
double f(double x, double y, double z) {
        double r65325 = y;
        double r65326 = x;
        double r65327 = z;
        double r65328 = r65326 - r65327;
        double r65329 = r65325 * r65328;
        double r65330 = 1.0;
        double r65331 = r65330 * r65327;
        double r65332 = r65329 + r65331;
        return r65332;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[z - \left(z - x\right) \cdot y\]

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot \left(1 - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  7. Taylor expanded around 0 0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019315 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

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

  (+ (* x y) (* z (- 1 y))))