Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[x \cdot y + 1 \cdot \left(z - x \cdot z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
x \cdot y + 1 \cdot \left(z - x \cdot z\right)
double f(double x, double y, double z) {
        double r202390 = x;
        double r202391 = y;
        double r202392 = r202390 * r202391;
        double r202393 = 1.0;
        double r202394 = r202393 - r202390;
        double r202395 = z;
        double r202396 = r202394 * r202395;
        double r202397 = r202392 + r202396;
        return r202397;
}
↓
double f(double x, double y, double z) {
        double r202398 = x;
        double r202399 = y;
        double r202400 = r202398 * r202399;
        double r202401 = 1.0;
        double r202402 = z;
        double r202403 = r202398 * r202402;
        double r202404 = r202402 - r202403;
        double r202405 = r202401 * r202404;
        double r202406 = r202400 + r202405;
        return r202406;
}

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

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

  3. Applied flip--8.0

    \[\leadsto x \cdot y + \color{blue}{\frac{1 \cdot 1 - x \cdot x}{1 + x}} \cdot z\]

  4. Applied associate-*l/10.1

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

  5. Taylor expanded around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019305 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1 x) z)))