Average Error: 3.2 → 3.1
Time: 4.3s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[x \cdot \left(1 - y \cdot z\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)\]
x \cdot \left(1 - y \cdot z\right)
↓
x \cdot \left(1 - y \cdot z\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)
double f(double x, double y, double z) {
        double r276161 = x;
        double r276162 = 1.0;
        double r276163 = y;
        double r276164 = z;
        double r276165 = r276163 * r276164;
        double r276166 = r276162 - r276165;
        double r276167 = r276161 * r276166;
        return r276167;
}
↓
double f(double x, double y, double z) {
        double r276168 = x;
        double r276169 = 1.0;
        double r276170 = y;
        double r276171 = z;
        double r276172 = r276170 * r276171;
        double r276173 = r276169 - r276172;
        double r276174 = r276168 * r276173;
        double r276175 = -r276171;
        double r276176 = r276171 * r276170;
        double r276177 = fma(r276175, r276170, r276176);
        double r276178 = r276168 * r276177;
        double r276179 = r276174 + r276178;
        return r276179;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 3.2

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

  3. Applied add-cube-cbrt3.2

    \[\leadsto x \cdot \left(\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}} - y \cdot z\right)\]

  4. Applied prod-diff3.2

    \[\leadsto x \cdot \color{blue}{\left(\mathsf{fma}\left(\sqrt[3]{1} \cdot \sqrt[3]{1}, \sqrt[3]{1}, -z \cdot y\right) + \mathsf{fma}\left(-z, y, z \cdot y\right)\right)}\]

  5. Applied distribute-lft-in3.1

    \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(\sqrt[3]{1} \cdot \sqrt[3]{1}, \sqrt[3]{1}, -z \cdot y\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)}\]

  6. Simplified3.1

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

  7. Final simplification3.1

    \[\leadsto x \cdot \left(1 - y \cdot z\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)\]

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1 (* y z))))