Average Error: 3.6 → 0.5
Time: 19.4s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -4.732351688106690578241563475637982249861 \cdot 10^{-110} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 5.803279721606684923513960024729438143599 \cdot 10^{-67}\right):\\ \;\;\;\;1 \cdot x + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
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):\\
\;\;\;\;1 \cdot x + \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 r639650 = x;
        double r639651 = 1.0;
        double r639652 = y;
        double r639653 = r639651 - r639652;
        double r639654 = z;
        double r639655 = r639653 * r639654;
        double r639656 = r639651 - r639655;
        double r639657 = r639650 * r639656;
        return r639657;
}
↓
double f(double x, double y, double z) {
        double r639658 = x;
        double r639659 = 1.0;
        double r639660 = y;
        double r639661 = r639659 - r639660;
        double r639662 = z;
        double r639663 = r639661 * r639662;
        double r639664 = r639659 - r639663;
        double r639665 = r639658 * r639664;
        double r639666 = -4.7323516881066906e-110;
        bool r639667 = r639665 <= r639666;
        double r639668 = 5.803279721606685e-67;
        bool r639669 = r639665 <= r639668;
        double r639670 = !r639669;
        bool r639671 = r639667 || r639670;
        double r639672 = r639659 * r639658;
        double r639673 = r639658 * r639662;
        double r639674 = r639660 - r639659;
        double r639675 = r639673 * r639674;
        double r639676 = r639672 + r639675;
        double r639677 = r639671 ? r639676 : r639665;
        return r639677;
}

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. Simplified4.8

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

    6. Simplified0.6

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

    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

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

Reproduce

herbie shell --seed 2019323 
(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))))