Average Error: 3.5 → 0.1
Time: 4.2s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.9634813897031917 \cdot 10^{-17} \lor \neg \left(z \le 1.102656055982303 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.9634813897031917 \cdot 10^{-17} \lor \neg \left(z \le 1.102656055982303 \cdot 10^{-48}\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 r914708 = x;
        double r914709 = 1.0;
        double r914710 = y;
        double r914711 = r914709 - r914710;
        double r914712 = z;
        double r914713 = r914711 * r914712;
        double r914714 = r914709 - r914713;
        double r914715 = r914708 * r914714;
        return r914715;
}
↓
double f(double x, double y, double z) {
        double r914716 = z;
        double r914717 = -5.963481389703192e-17;
        bool r914718 = r914716 <= r914717;
        double r914719 = 1.102656055982303e-48;
        bool r914720 = r914716 <= r914719;
        double r914721 = !r914720;
        bool r914722 = r914718 || r914721;
        double r914723 = x;
        double r914724 = 1.0;
        double r914725 = r914723 * r914724;
        double r914726 = r914723 * r914716;
        double r914727 = y;
        double r914728 = r914727 - r914724;
        double r914729 = r914726 * r914728;
        double r914730 = r914725 + r914729;
        double r914731 = r914724 - r914727;
        double r914732 = r914731 * r914716;
        double r914733 = r914724 - r914732;
        double r914734 = r914723 * r914733;
        double r914735 = r914722 ? r914730 : r914734;
        return r914735;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -5.963481389703192e-17 or 1.102656055982303e-48 < z

    1. Initial program 7.6

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

    3. Applied sub-neg7.6

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

    4. Applied distribute-lft-in7.6

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

    5. Simplified0.2

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

    if -5.963481389703192e-17 < z < 1.102656055982303e-48

    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 simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.9634813897031917 \cdot 10^{-17} \lor \neg \left(z \le 1.102656055982303 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 +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))))