Average Error: 0.0 → 0.0
Time: 19.8s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\left(z \cdot y + x\right) - x \cdot z\]
x + \left(y - x\right) \cdot z
↓
\left(z \cdot y + x\right) - x \cdot z
double f(double x, double y, double z) {
        double r149627 = x;
        double r149628 = y;
        double r149629 = r149628 - r149627;
        double r149630 = z;
        double r149631 = r149629 * r149630;
        double r149632 = r149627 + r149631;
        return r149632;
}
↓
double f(double x, double y, double z) {
        double r149633 = z;
        double r149634 = y;
        double r149635 = r149633 * r149634;
        double r149636 = x;
        double r149637 = r149635 + r149636;
        double r149638 = r149636 * r149633;
        double r149639 = r149637 - r149638;
        return r149639;
}

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

Derivation

  1. Initial program 0.0

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

  3. Applied flip-+29.6

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

  5. Applied associate-*r*31.8

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

  6. Taylor expanded around 0 0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))