Average Error: 3.8 → 0.4
Time: 4.5s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.821134117448161 \cdot 10^{131} \lor \neg \left(z \le 2.6179480675622549 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.821134117448161 \cdot 10^{131} \lor \neg \left(z \le 2.6179480675622549 \cdot 10^{-20}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r723589 = x;
        double r723590 = 1.0;
        double r723591 = y;
        double r723592 = r723590 - r723591;
        double r723593 = z;
        double r723594 = r723592 * r723593;
        double r723595 = r723590 - r723594;
        double r723596 = r723589 * r723595;
        return r723596;
}
↓
double f(double x, double y, double z) {
        double r723597 = z;
        double r723598 = -5.821134117448161e+131;
        bool r723599 = r723597 <= r723598;
        double r723600 = 2.617948067562255e-20;
        bool r723601 = r723597 <= r723600;
        double r723602 = !r723601;
        bool r723603 = r723599 || r723602;
        double r723604 = x;
        double r723605 = 1.0;
        double r723606 = r723604 * r723605;
        double r723607 = r723604 * r723597;
        double r723608 = y;
        double r723609 = r723608 - r723605;
        double r723610 = r723607 * r723609;
        double r723611 = r723606 + r723610;
        double r723612 = r723605 - r723608;
        double r723613 = r723612 * r723597;
        double r723614 = r723605 - r723613;
        double r723615 = r723604 * r723614;
        double r723616 = r723603 ? r723611 : r723615;
        return r723616;
}

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

Target

Original3.8
Target0.3
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.821134117448161e+131 or 2.617948067562255e-20 < z

    1. Initial program 10.9

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

    3. Applied sub-neg10.9

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

    4. Applied distribute-lft-in10.9

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

    5. Simplified0.1

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

    if -5.821134117448161e+131 < z < 2.617948067562255e-20

    1. Initial program 0.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.821134117448161 \cdot 10^{131} \lor \neg \left(z \le 2.6179480675622549 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1 (* (- 1 y) z))) -1.618195973607049e+50) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x)))))

  (* x (- 1 (* (- 1 y) z))))