Average Error: 3.6 → 0.5
Time: 23.9s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -4.732351688106690578241563475637982249861 \cdot 10^{-110} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 5.803279721606684923513960024729438143599 \cdot 10^{-67}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
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 -4.732351688106690578241563475637982249861 \cdot 10^{-110} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 5.803279721606684923513960024729438143599 \cdot 10^{-67}\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 r520849 = x;
        double r520850 = 1.0;
        double r520851 = y;
        double r520852 = r520850 - r520851;
        double r520853 = z;
        double r520854 = r520852 * r520853;
        double r520855 = r520850 - r520854;
        double r520856 = r520849 * r520855;
        return r520856;
}
↓
double f(double x, double y, double z) {
        double r520857 = x;
        double r520858 = 1.0;
        double r520859 = y;
        double r520860 = r520858 - r520859;
        double r520861 = z;
        double r520862 = r520860 * r520861;
        double r520863 = r520858 - r520862;
        double r520864 = r520857 * r520863;
        double r520865 = -4.7323516881066906e-110;
        bool r520866 = r520864 <= r520865;
        double r520867 = 5.803279721606685e-67;
        bool r520868 = r520864 <= r520867;
        double r520869 = !r520868;
        bool r520870 = r520866 || r520869;
        double r520871 = r520857 * r520858;
        double r520872 = r520857 * r520861;
        double r520873 = r520859 - r520858;
        double r520874 = r520872 * r520873;
        double r520875 = r520871 + r520874;
        double r520876 = r520870 ? r520875 : r520864;
        return r520876;
}

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

Original3.6
Target0.3
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.892237649663902900973248011051357504727 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (- 1.0 (* (- 1.0 y) z))) < -4.7323516881066906e-110 or 5.803279721606685e-67 < (* x (- 1.0 (* (- 1.0 y) z)))

    1. Initial program 4.8

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

    3. Applied sub-neg4.8

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

    4. Applied distribute-lft-in4.8

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

    5. Simplified0.6

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

    if -4.7323516881066906e-110 < (* x (- 1.0 (* (- 1.0 y) z))) < 5.803279721606685e-67

    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 simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -4.732351688106690578241563475637982249861 \cdot 10^{-110} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 5.803279721606684923513960024729438143599 \cdot 10^{-67}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +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))))