Average Error: 3.7 → 0.1
Time: 4.6s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -1.549569963444854001412453568724587510933 \cdot 10^{203}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \le 1.946618348255187764452186866922445476636 \cdot 10^{304}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(\left(\left(\left(x \cdot z\right) \cdot \sqrt[3]{y - 1}\right) \cdot \sqrt[3]{\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}}\right) \cdot \sqrt[3]{\sqrt[3]{y - 1}}\right) \cdot \sqrt[3]{y - 1}\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(1 - y\right) \cdot z \le -1.549569963444854001412453568724587510933 \cdot 10^{203}:\\
\;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\

\mathbf{elif}\;\left(1 - y\right) \cdot z \le 1.946618348255187764452186866922445476636 \cdot 10^{304}:\\
\;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot 1 + \left(\left(\left(\left(x \cdot z\right) \cdot \sqrt[3]{y - 1}\right) \cdot \sqrt[3]{\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}}\right) \cdot \sqrt[3]{\sqrt[3]{y - 1}}\right) \cdot \sqrt[3]{y - 1}\\

\end{array}
double f(double x, double y, double z) {
        double r862902 = x;
        double r862903 = 1.0;
        double r862904 = y;
        double r862905 = r862903 - r862904;
        double r862906 = z;
        double r862907 = r862905 * r862906;
        double r862908 = r862903 - r862907;
        double r862909 = r862902 * r862908;
        return r862909;
}
↓
double f(double x, double y, double z) {
        double r862910 = 1.0;
        double r862911 = y;
        double r862912 = r862910 - r862911;
        double r862913 = z;
        double r862914 = r862912 * r862913;
        double r862915 = -1.549569963444854e+203;
        bool r862916 = r862914 <= r862915;
        double r862917 = x;
        double r862918 = r862917 * r862910;
        double r862919 = r862917 * r862913;
        double r862920 = r862911 - r862910;
        double r862921 = r862919 * r862920;
        double r862922 = r862918 + r862921;
        double r862923 = 1.9466183482551878e+304;
        bool r862924 = r862914 <= r862923;
        double r862925 = r862910 - r862914;
        double r862926 = r862917 * r862925;
        double r862927 = cbrt(r862920);
        double r862928 = r862919 * r862927;
        double r862929 = r862927 * r862927;
        double r862930 = cbrt(r862929);
        double r862931 = r862928 * r862930;
        double r862932 = cbrt(r862927);
        double r862933 = r862931 * r862932;
        double r862934 = r862933 * r862927;
        double r862935 = r862918 + r862934;
        double r862936 = r862924 ? r862926 : r862935;
        double r862937 = r862916 ? r862922 : r862936;
        return r862937;
}

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

Derivation

  1. Split input into 3 regimes

  2. if (* (- 1.0 y) z) < -1.549569963444854e+203

    1. Initial program 20.2

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

    3. Applied sub-neg20.2

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

    4. Applied distribute-lft-in20.2

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

    5. Simplified0.3

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

    if -1.549569963444854e+203 < (* (- 1.0 y) z) < 1.9466183482551878e+304

    1. Initial program 0.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]

    if 1.9466183482551878e+304 < (* (- 1.0 y) z)

    1. Initial program 60.4

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

    3. Applied sub-neg60.4

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

    4. Applied distribute-lft-in60.4

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

    5. Simplified0.3

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

    7. Applied add-cube-cbrt1.2

      \[\leadsto x \cdot 1 + \left(x \cdot z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right) \cdot \sqrt[3]{y - 1}\right)}\]

    8. Applied associate-*r*1.2

      \[\leadsto x \cdot 1 + \color{blue}{\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right)\right) \cdot \sqrt[3]{y - 1}}\]
    9. Using strategy rm

    10. Applied associate-*r*1.2

      \[\leadsto x \cdot 1 + \color{blue}{\left(\left(\left(x \cdot z\right) \cdot \sqrt[3]{y - 1}\right) \cdot \sqrt[3]{y - 1}\right)} \cdot \sqrt[3]{y - 1}\]
    11. Using strategy rm

    12. Applied add-cube-cbrt1.3

      \[\leadsto x \cdot 1 + \left(\left(\left(x \cdot z\right) \cdot \sqrt[3]{y - 1}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}\right) \cdot \sqrt[3]{y - 1}}}\right) \cdot \sqrt[3]{y - 1}\]

    13. Applied cbrt-prod1.4

      \[\leadsto x \cdot 1 + \left(\left(\left(x \cdot z\right) \cdot \sqrt[3]{y - 1}\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}} \cdot \sqrt[3]{\sqrt[3]{y - 1}}\right)}\right) \cdot \sqrt[3]{y - 1}\]

    14. Applied associate-*r*1.4

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -1.549569963444854001412453568724587510933 \cdot 10^{203}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \le 1.946618348255187764452186866922445476636 \cdot 10^{304}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(\left(\left(\left(x \cdot z\right) \cdot \sqrt[3]{y - 1}\right) \cdot \sqrt[3]{\sqrt[3]{y - 1} \cdot \sqrt[3]{y - 1}}\right) \cdot \sqrt[3]{\sqrt[3]{y - 1}}\right) \cdot \sqrt[3]{y - 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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))))