Average Error: 3.1 → 0.3
Time: 4.2s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -2.7437084799844819580695733533950081391 \cdot 10^{126} \lor \neg \left(\left(1 - y\right) \cdot z \le 1.051043436711480859733686334481019387972 \cdot 10^{168}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(1 - y\right) \cdot z \le -2.7437084799844819580695733533950081391 \cdot 10^{126} \lor \neg \left(\left(1 - y\right) \cdot z \le 1.051043436711480859733686334481019387972 \cdot 10^{168}\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 r868161 = x;
        double r868162 = 1.0;
        double r868163 = y;
        double r868164 = r868162 - r868163;
        double r868165 = z;
        double r868166 = r868164 * r868165;
        double r868167 = r868162 - r868166;
        double r868168 = r868161 * r868167;
        return r868168;
}
↓
double f(double x, double y, double z) {
        double r868169 = 1.0;
        double r868170 = y;
        double r868171 = r868169 - r868170;
        double r868172 = z;
        double r868173 = r868171 * r868172;
        double r868174 = -2.743708479984482e+126;
        bool r868175 = r868173 <= r868174;
        double r868176 = 1.0510434367114809e+168;
        bool r868177 = r868173 <= r868176;
        double r868178 = !r868177;
        bool r868179 = r868175 || r868178;
        double r868180 = x;
        double r868181 = r868180 * r868169;
        double r868182 = r868180 * r868172;
        double r868183 = r868170 - r868169;
        double r868184 = r868182 * r868183;
        double r868185 = r868181 + r868184;
        double r868186 = r868169 - r868173;
        double r868187 = r868180 * r868186;
        double r868188 = r868179 ? r868185 : r868187;
        return r868188;
}

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

Original3.1
Target0.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.892237649663902900973248011051357504727 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- 1.0 y) z) < -2.743708479984482e+126 or 1.0510434367114809e+168 < (* (- 1.0 y) z)

    1. Initial program 11.9

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

    3. Applied sub-neg11.9

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

    4. Applied distribute-lft-in11.9

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

    5. Simplified1.0

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

    if -2.743708479984482e+126 < (* (- 1.0 y) z) < 1.0510434367114809e+168

    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 simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -2.7437084799844819580695733533950081391 \cdot 10^{126} \lor \neg \left(\left(1 - y\right) \cdot z \le 1.051043436711480859733686334481019387972 \cdot 10^{168}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019356 
(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))))