Average Error: 3.2 → 0.2
Time: 1.8s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \le -6.4934052504044776 \cdot 10^{306} \lor \neg \left(y \cdot z \le 3.0707001026583607 \cdot 10^{167}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(-y \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - y \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z \le -6.4934052504044776 \cdot 10^{306} \lor \neg \left(y \cdot z \le 3.0707001026583607 \cdot 10^{167}\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 r224287 = x;
        double r224288 = 1.0;
        double r224289 = y;
        double r224290 = z;
        double r224291 = r224289 * r224290;
        double r224292 = r224288 - r224291;
        double r224293 = r224287 * r224292;
        return r224293;
}
↓
double f(double x, double y, double z) {
        double r224294 = y;
        double r224295 = z;
        double r224296 = r224294 * r224295;
        double r224297 = -6.493405250404478e+306;
        bool r224298 = r224296 <= r224297;
        double r224299 = 3.0707001026583607e+167;
        bool r224300 = r224296 <= r224299;
        double r224301 = !r224300;
        bool r224302 = r224298 || r224301;
        double r224303 = x;
        double r224304 = 1.0;
        double r224305 = r224303 * r224304;
        double r224306 = r224303 * r224294;
        double r224307 = -r224295;
        double r224308 = r224306 * r224307;
        double r224309 = r224305 + r224308;
        double r224310 = -r224296;
        double r224311 = r224303 * r224310;
        double r224312 = r224305 + r224311;
        double r224313 = r224302 ? r224309 : r224312;
        return r224313;
}

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) < -6.493405250404478e+306 or 3.0707001026583607e+167 < (* y z)

    1. Initial program 32.9

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

    3. Applied sub-neg32.9

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

    4. Applied distribute-lft-in32.9

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

    6. Applied distribute-rgt-neg-in32.9

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

    7. Applied associate-*r*1.1

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

    if -6.493405250404478e+306 < (* y z) < 3.0707001026583607e+167

    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 simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \le -6.4934052504044776 \cdot 10^{306} \lor \neg \left(y \cdot z \le 3.0707001026583607 \cdot 10^{167}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(-y \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +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))))