Average Error: 3.5 → 0.2
Time: 3.4s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.29202225383303388 \cdot 10^{-98} \lor \neg \left(z \le 6.423048079579083 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.29202225383303388 \cdot 10^{-98} \lor \neg \left(z \le 6.423048079579083 \cdot 10^{-46}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r1553633 = x;
        double r1553634 = 1.0;
        double r1553635 = y;
        double r1553636 = r1553634 - r1553635;
        double r1553637 = z;
        double r1553638 = r1553636 * r1553637;
        double r1553639 = r1553634 - r1553638;
        double r1553640 = r1553633 * r1553639;
        return r1553640;
}
↓
double f(double x, double y, double z) {
        double r1553641 = z;
        double r1553642 = -1.2920222538330339e-98;
        bool r1553643 = r1553641 <= r1553642;
        double r1553644 = 6.423048079579083e-46;
        bool r1553645 = r1553641 <= r1553644;
        double r1553646 = !r1553645;
        bool r1553647 = r1553643 || r1553646;
        double r1553648 = x;
        double r1553649 = 1.0;
        double r1553650 = r1553648 * r1553649;
        double r1553651 = r1553648 * r1553641;
        double r1553652 = y;
        double r1553653 = r1553652 - r1553649;
        double r1553654 = r1553651 * r1553653;
        double r1553655 = r1553650 + r1553654;
        double r1553656 = r1553641 * r1553652;
        double r1553657 = r1553648 * r1553656;
        double r1553658 = -r1553649;
        double r1553659 = r1553651 * r1553658;
        double r1553660 = r1553657 + r1553659;
        double r1553661 = r1553650 + r1553660;
        double r1553662 = r1553647 ? r1553655 : r1553661;
        return r1553662;
}

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

Original3.5
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.2920222538330339e-98 or 6.423048079579083e-46 < z

    1. Initial program 6.5

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

    3. Applied sub-neg6.5

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

    4. Applied distribute-lft-in6.5

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

    5. Simplified0.3

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

    if -1.2920222538330339e-98 < z < 6.423048079579083e-46

    1. Initial program 0.1

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

    3. Applied sub-neg0.1

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

    4. Applied distribute-lft-in0.1

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

    5. Simplified2.7

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

    7. Applied sub-neg2.7

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

    8. Applied distribute-lft-in2.7

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

    9. Simplified0.1

      \[\leadsto x \cdot 1 + \left(\color{blue}{x \cdot \left(z \cdot y\right)} + \left(x \cdot z\right) \cdot \left(-1\right)\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.29202225383303388 \cdot 10^{-98} \lor \neg \left(z \le 6.423048079579083 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 +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))))