Average Error: 3.1 → 0.5
Time: 3.3s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \le -6.17769750561453994 \cdot 10^{121} \lor \neg \left(y \cdot z \le 7.17200634455581739 \cdot 10^{212}\right):\\ \;\;\;\;x \cdot 1 + \left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - y \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z \le -6.17769750561453994 \cdot 10^{121} \lor \neg \left(y \cdot z \le 7.17200634455581739 \cdot 10^{212}\right):\\
\;\;\;\;x \cdot 1 + \left(\left(-x\right) \cdot y\right) \cdot z\\

\mathbf{else}:\\
\;\;\;\;x \cdot \left(1 - y \cdot z\right)\\

\end{array}
double f(double x, double y, double z) {
        double r290714 = x;
        double r290715 = 1.0;
        double r290716 = y;
        double r290717 = z;
        double r290718 = r290716 * r290717;
        double r290719 = r290715 - r290718;
        double r290720 = r290714 * r290719;
        return r290720;
}
↓
double f(double x, double y, double z) {
        double r290721 = y;
        double r290722 = z;
        double r290723 = r290721 * r290722;
        double r290724 = -6.17769750561454e+121;
        bool r290725 = r290723 <= r290724;
        double r290726 = 7.172006344555817e+212;
        bool r290727 = r290723 <= r290726;
        double r290728 = !r290727;
        bool r290729 = r290725 || r290728;
        double r290730 = x;
        double r290731 = 1.0;
        double r290732 = r290730 * r290731;
        double r290733 = -r290730;
        double r290734 = r290733 * r290721;
        double r290735 = r290734 * r290722;
        double r290736 = r290732 + r290735;
        double r290737 = r290731 - r290723;
        double r290738 = r290730 * r290737;
        double r290739 = r290729 ? r290736 : r290738;
        return r290739;
}

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. Split input into 2 regimes

  2. if (* y z) < -6.17769750561454e+121 or 7.172006344555817e+212 < (* y z)

    1. Initial program 18.6

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

    3. Applied add-cube-cbrt19.5

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

    4. Applied associate-*l*19.5

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

    6. Applied sub-neg19.5

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

    7. Applied distribute-lft-in19.5

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

    8. Applied distribute-lft-in19.5

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

    9. Simplified19.5

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

    10. Simplified18.6

      \[\leadsto x \cdot 1 + \color{blue}{\left(-x\right) \cdot \left(y \cdot z\right)}\]
    11. Using strategy rm

    12. Applied associate-*r*2.7

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

    if -6.17769750561454e+121 < (* y z) < 7.172006344555817e+212

    1. Initial program 0.1

      \[x \cdot \left(1 - y \cdot z\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \le -6.17769750561453994 \cdot 10^{121} \lor \neg \left(y \cdot z \le 7.17200634455581739 \cdot 10^{212}\right):\\ \;\;\;\;x \cdot 1 + \left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1 (* y z))))