Average Error: 3.2 → 3.2
Time: 2.5s
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 r229030 = x;
        double r229031 = 1.0;
        double r229032 = y;
        double r229033 = z;
        double r229034 = r229032 * r229033;
        double r229035 = r229031 - r229034;
        double r229036 = r229030 * r229035;
        return r229036;
}
↓
double f(double x, double y, double z) {
        double r229037 = x;
        double r229038 = 1.0;
        double r229039 = y;
        double r229040 = z;
        double r229041 = r229039 * r229040;
        double r229042 = r229038 - r229041;
        double r229043 = r229037 * r229042;
        double r229044 = -r229040;
        double r229045 = r229040 * r229039;
        double r229046 = fma(r229044, r229039, r229045);
        double r229047 = r229037 * r229046;
        double r229048 = r229043 + r229047;
        return r229048;
}

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-in3.2

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

  6. Simplified3.2

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

  7. Final simplification3.2

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

Reproduce

herbie shell --seed 2020025 +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))))