Average Error: 0.0 → 0.0
Time: 40.1s
Precision: 64
\[x \cdot y + \left(1.0 - x\right) \cdot z\]
↓
\[z \cdot 1.0 + x \cdot \left(y - z\right)\]
x \cdot y + \left(1.0 - x\right) \cdot z
↓
z \cdot 1.0 + x \cdot \left(y - z\right)
double f(double x, double y, double z) {
        double r10164310 = x;
        double r10164311 = y;
        double r10164312 = r10164310 * r10164311;
        double r10164313 = 1.0;
        double r10164314 = r10164313 - r10164310;
        double r10164315 = z;
        double r10164316 = r10164314 * r10164315;
        double r10164317 = r10164312 + r10164316;
        return r10164317;
}
↓
double f(double x, double y, double z) {
        double r10164318 = z;
        double r10164319 = 1.0;
        double r10164320 = r10164318 * r10164319;
        double r10164321 = x;
        double r10164322 = y;
        double r10164323 = r10164322 - r10164318;
        double r10164324 = r10164321 * r10164323;
        double r10164325 = r10164320 + r10164324;
        return r10164325;
}

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

    \[x \cdot y + \left(1.0 - x\right) \cdot z\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(1.0 \cdot z + x \cdot y\right) - x \cdot z}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{z \cdot 1.0 + x \cdot \left(y - z\right)}\]

  4. Final simplification0.0

    \[\leadsto z \cdot 1.0 + x \cdot \left(y - z\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))