Average Error: 0.0 → 0.0
Time: 7.2s
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 r455691 = x;
        double r455692 = y;
        double r455693 = r455691 * r455692;
        double r455694 = z;
        double r455695 = 1.0;
        double r455696 = r455695 - r455692;
        double r455697 = r455694 * r455696;
        double r455698 = r455693 + r455697;
        return r455698;
}
↓
double f(double x, double y, double z) {
        double r455699 = y;
        double r455700 = x;
        double r455701 = z;
        double r455702 = r455700 - r455701;
        double r455703 = r455699 * r455702;
        double r455704 = 1.0;
        double r455705 = r455704 * r455701;
        double r455706 = r455703 + r455705;
        return r455706;
}

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-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  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 2019306 
(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))))