Average Error: 3.2 → 0.2
Time: 6.0s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z = -\infty \lor \neg \left(\left(1 - y\right) \cdot z \le 1.255058086158299250292400775229495012975 \cdot 10^{159}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(1 - y\right) \cdot z = -\infty \lor \neg \left(\left(1 - y\right) \cdot z \le 1.255058086158299250292400775229495012975 \cdot 10^{159}\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 r904728 = x;
        double r904729 = 1.0;
        double r904730 = y;
        double r904731 = r904729 - r904730;
        double r904732 = z;
        double r904733 = r904731 * r904732;
        double r904734 = r904729 - r904733;
        double r904735 = r904728 * r904734;
        return r904735;
}
↓
double f(double x, double y, double z) {
        double r904736 = 1.0;
        double r904737 = y;
        double r904738 = r904736 - r904737;
        double r904739 = z;
        double r904740 = r904738 * r904739;
        double r904741 = -inf.0;
        bool r904742 = r904740 <= r904741;
        double r904743 = 1.2550580861582993e+159;
        bool r904744 = r904740 <= r904743;
        double r904745 = !r904744;
        bool r904746 = r904742 || r904745;
        double r904747 = x;
        double r904748 = r904747 * r904736;
        double r904749 = r904747 * r904739;
        double r904750 = r904737 - r904736;
        double r904751 = r904749 * r904750;
        double r904752 = r904748 + r904751;
        double r904753 = r904739 * r904737;
        double r904754 = r904747 * r904753;
        double r904755 = -r904736;
        double r904756 = r904749 * r904755;
        double r904757 = r904754 + r904756;
        double r904758 = r904748 + r904757;
        double r904759 = r904746 ? r904752 : r904758;
        return r904759;
}

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

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

Derivation

  1. Split input into 2 regimes

  2. if (* (- 1.0 y) z) < -inf.0 or 1.2550580861582993e+159 < (* (- 1.0 y) z)

    1. Initial program 22.6

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

    3. Applied sub-neg22.6

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

    4. Applied distribute-lft-in22.6

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

    5. Simplified0.7

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

    if -inf.0 < (* (- 1.0 y) z) < 1.2550580861582993e+159

    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. Simplified2.0

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

    7. Applied sub-neg2.0

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

    8. Applied distribute-lft-in2.0

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

    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z = -\infty \lor \neg \left(\left(1 - y\right) \cdot z \le 1.255058086158299250292400775229495012975 \cdot 10^{159}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 +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))))