Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[z \cdot 1 + x \cdot \left(y - z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
z \cdot 1 + x \cdot \left(y - z\right)
double f(double x, double y, double z) {
        double r10362749 = x;
        double r10362750 = y;
        double r10362751 = r10362749 * r10362750;
        double r10362752 = 1.0;
        double r10362753 = r10362752 - r10362749;
        double r10362754 = z;
        double r10362755 = r10362753 * r10362754;
        double r10362756 = r10362751 + r10362755;
        return r10362756;
}
↓
double f(double x, double y, double z) {
        double r10362757 = z;
        double r10362758 = 1.0;
        double r10362759 = r10362757 * r10362758;
        double r10362760 = x;
        double r10362761 = y;
        double r10362762 = r10362761 - r10362757;
        double r10362763 = r10362760 * r10362762;
        double r10362764 = r10362759 + r10362763;
        return r10362764;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))