Average Error: 3.4 → 0.1
Time: 4.2s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -1.0085285988747638 \cdot 10^{148} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 5.2909404280952141 \cdot 10^{50}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -1.0085285988747638 \cdot 10^{148} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 5.2909404280952141 \cdot 10^{50}\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 r809815 = x;
        double r809816 = 1.0;
        double r809817 = y;
        double r809818 = r809816 - r809817;
        double r809819 = z;
        double r809820 = r809818 * r809819;
        double r809821 = r809816 - r809820;
        double r809822 = r809815 * r809821;
        return r809822;
}
↓
double f(double x, double y, double z) {
        double r809823 = x;
        double r809824 = 1.0;
        double r809825 = y;
        double r809826 = r809824 - r809825;
        double r809827 = z;
        double r809828 = r809826 * r809827;
        double r809829 = r809824 - r809828;
        double r809830 = r809823 * r809829;
        double r809831 = -1.0085285988747638e+148;
        bool r809832 = r809830 <= r809831;
        double r809833 = 5.290940428095214e+50;
        bool r809834 = r809830 <= r809833;
        double r809835 = !r809834;
        bool r809836 = r809832 || r809835;
        double r809837 = r809823 * r809824;
        double r809838 = r809823 * r809827;
        double r809839 = r809825 - r809824;
        double r809840 = r809838 * r809839;
        double r809841 = r809837 + r809840;
        double r809842 = r809836 ? r809841 : r809830;
        return r809842;
}

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

Original3.4
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 (* x (- 1.0 (* (- 1.0 y) z))) < -1.0085285988747638e+148 or 5.290940428095214e+50 < (* x (- 1.0 (* (- 1.0 y) z)))

    1. Initial program 8.0

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

    3. Applied sub-neg8.0

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

    4. Applied distribute-lft-in8.0

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

    5. Simplified0.1

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

    if -1.0085285988747638e+148 < (* x (- 1.0 (* (- 1.0 y) z))) < 5.290940428095214e+50

    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -1.0085285988747638 \cdot 10^{148} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 5.2909404280952141 \cdot 10^{50}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(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))))