Average Error: 3.4 → 0.9
Time: 2.3s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \le -1.6429161822787508 \cdot 10^{58} \lor \neg \left(y \cdot z \le 1.1216381272031817 \cdot 10^{279}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(-y \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - y \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z \le -1.6429161822787508 \cdot 10^{58} \lor \neg \left(y \cdot z \le 1.1216381272031817 \cdot 10^{279}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot y\right) \cdot \left(-z\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r232353 = x;
        double r232354 = 1.0;
        double r232355 = y;
        double r232356 = z;
        double r232357 = r232355 * r232356;
        double r232358 = r232354 - r232357;
        double r232359 = r232353 * r232358;
        return r232359;
}
↓
double f(double x, double y, double z) {
        double r232360 = y;
        double r232361 = z;
        double r232362 = r232360 * r232361;
        double r232363 = -1.6429161822787508e+58;
        bool r232364 = r232362 <= r232363;
        double r232365 = 1.1216381272031817e+279;
        bool r232366 = r232362 <= r232365;
        double r232367 = !r232366;
        bool r232368 = r232364 || r232367;
        double r232369 = x;
        double r232370 = 1.0;
        double r232371 = r232369 * r232370;
        double r232372 = r232369 * r232360;
        double r232373 = -r232361;
        double r232374 = r232372 * r232373;
        double r232375 = r232371 + r232374;
        double r232376 = -r232362;
        double r232377 = r232369 * r232376;
        double r232378 = r232371 + r232377;
        double r232379 = r232368 ? r232375 : r232378;
        return r232379;
}

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) < -1.6429161822787508e+58 or 1.1216381272031817e+279 < (* y z)

    1. Initial program 18.1

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

    3. Applied sub-neg18.1

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

    4. Applied distribute-lft-in18.1

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

    6. Applied distribute-rgt-neg-in18.1

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

    7. Applied associate-*r*4.7

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

    if -1.6429161822787508e+58 < (* y z) < 1.1216381272031817e+279

    1. Initial program 0.1

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

    3. Applied sub-neg0.1

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

    4. Applied distribute-lft-in0.1

      \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-y \cdot z\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \le -1.6429161822787508 \cdot 10^{58} \lor \neg \left(y \cdot z \le 1.1216381272031817 \cdot 10^{279}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(-y \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +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))))