Average Error: 3.7 → 0.1
Time: 4.3s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -1.51187660485705172 \cdot 10^{247} \lor \neg \left(\left(1 - y\right) \cdot z \le 4.1069068715318459 \cdot 10^{200}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(1 - y\right) \cdot z \le -1.51187660485705172 \cdot 10^{247} \lor \neg \left(\left(1 - y\right) \cdot z \le 4.1069068715318459 \cdot 10^{200}\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 r722639 = x;
        double r722640 = 1.0;
        double r722641 = y;
        double r722642 = r722640 - r722641;
        double r722643 = z;
        double r722644 = r722642 * r722643;
        double r722645 = r722640 - r722644;
        double r722646 = r722639 * r722645;
        return r722646;
}
↓
double f(double x, double y, double z) {
        double r722647 = 1.0;
        double r722648 = y;
        double r722649 = r722647 - r722648;
        double r722650 = z;
        double r722651 = r722649 * r722650;
        double r722652 = -1.5118766048570517e+247;
        bool r722653 = r722651 <= r722652;
        double r722654 = 4.106906871531846e+200;
        bool r722655 = r722651 <= r722654;
        double r722656 = !r722655;
        bool r722657 = r722653 || r722656;
        double r722658 = x;
        double r722659 = r722658 * r722647;
        double r722660 = r722658 * r722650;
        double r722661 = r722648 - r722647;
        double r722662 = r722660 * r722661;
        double r722663 = r722659 + r722662;
        double r722664 = r722647 - r722651;
        double r722665 = r722658 * r722664;
        double r722666 = r722657 ? r722663 : r722665;
        return r722666;
}

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

Original3.7
Target0.2
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- 1.0 y) z) < -1.5118766048570517e+247 or 4.106906871531846e+200 < (* (- 1.0 y) z)

    1. Initial program 23.1

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

    3. Applied sub-neg23.1

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

    4. Applied distribute-lft-in23.1

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

    5. Simplified0.4

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

    if -1.5118766048570517e+247 < (* (- 1.0 y) z) < 4.106906871531846e+200

    1. Initial program 0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -1.51187660485705172 \cdot 10^{247} \lor \neg \left(\left(1 - y\right) \cdot z \le 4.1069068715318459 \cdot 10^{200}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(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))))