Average Error: 0.0 → 0.0
Time: 3.5s
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 r223934 = x;
        double r223935 = y;
        double r223936 = r223934 * r223935;
        double r223937 = 1.0;
        double r223938 = r223937 - r223934;
        double r223939 = z;
        double r223940 = r223938 * r223939;
        double r223941 = r223936 + r223940;
        return r223941;
}
↓
double f(double x, double y, double z) {
        double r223942 = x;
        double r223943 = y;
        double r223944 = r223942 * r223943;
        double r223945 = 1.0;
        double r223946 = z;
        double r223947 = r223942 * r223946;
        double r223948 = r223946 - r223947;
        double r223949 = r223945 * r223948;
        double r223950 = r223944 + r223949;
        return r223950;
}

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--7.6

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

  4. Applied associate-*l/9.8

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

  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 2020018 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1 x) z)))