Average Error: 3.5 → 2.0
Time: 14.8s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \le 1.504828077239251210599676853555794383052 \cdot 10^{159}:\\ \;\;\;\;1 \cdot x + \left(-y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x + y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array}\]
x \cdot \left(1 - y \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z \le 1.504828077239251210599676853555794383052 \cdot 10^{159}:\\
\;\;\;\;1 \cdot x + \left(-y \cdot z\right) \cdot x\\

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

\end{array}
double f(double x, double y, double z) {
        double r185244 = x;
        double r185245 = 1.0;
        double r185246 = y;
        double r185247 = z;
        double r185248 = r185246 * r185247;
        double r185249 = r185245 - r185248;
        double r185250 = r185244 * r185249;
        return r185250;
}
↓
double f(double x, double y, double z) {
        double r185251 = y;
        double r185252 = z;
        double r185253 = r185251 * r185252;
        double r185254 = 1.5048280772392512e+159;
        bool r185255 = r185253 <= r185254;
        double r185256 = 1.0;
        double r185257 = x;
        double r185258 = r185256 * r185257;
        double r185259 = -r185253;
        double r185260 = r185259 * r185257;
        double r185261 = r185258 + r185260;
        double r185262 = -r185257;
        double r185263 = r185252 * r185262;
        double r185264 = r185251 * r185263;
        double r185265 = r185258 + r185264;
        double r185266 = r185255 ? r185261 : r185265;
        return r185266;
}

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) < 1.5048280772392512e+159

    1. Initial program 1.9

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

    3. Applied sub-neg1.9

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

    4. Applied distribute-lft-in1.9

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

    5. Simplified1.9

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

    6. Simplified1.9

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

    if 1.5048280772392512e+159 < (* y z)

    1. Initial program 22.7

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

    3. Applied sub-neg22.7

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

    4. Applied distribute-lft-in22.7

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

    5. Simplified22.7

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

    6. Simplified22.7

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

    8. Applied distribute-rgt-neg-in22.7

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

    9. Applied associate-*l*2.6

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

    10. Simplified2.6

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \le 1.504828077239251210599676853555794383052 \cdot 10^{159}:\\ \;\;\;\;1 \cdot x + \left(-y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x + y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +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))))