Average Error: 3.4 → 0.3
Time: 4.0s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;1 - \left(1 - y\right) \cdot z \le -2.3842446993784196 \cdot 10^{131} \lor \neg \left(1 - \left(1 - y\right) \cdot z \le 6.0335465209293531 \cdot 10^{306}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;1 - \left(1 - y\right) \cdot z \le -2.3842446993784196 \cdot 10^{131} \lor \neg \left(1 - \left(1 - y\right) \cdot z \le 6.0335465209293531 \cdot 10^{306}\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 r910071 = x;
        double r910072 = 1.0;
        double r910073 = y;
        double r910074 = r910072 - r910073;
        double r910075 = z;
        double r910076 = r910074 * r910075;
        double r910077 = r910072 - r910076;
        double r910078 = r910071 * r910077;
        return r910078;
}
↓
double f(double x, double y, double z) {
        double r910079 = 1.0;
        double r910080 = y;
        double r910081 = r910079 - r910080;
        double r910082 = z;
        double r910083 = r910081 * r910082;
        double r910084 = r910079 - r910083;
        double r910085 = -2.3842446993784196e+131;
        bool r910086 = r910084 <= r910085;
        double r910087 = 6.033546520929353e+306;
        bool r910088 = r910084 <= r910087;
        double r910089 = !r910088;
        bool r910090 = r910086 || r910089;
        double r910091 = x;
        double r910092 = r910091 * r910079;
        double r910093 = r910091 * r910082;
        double r910094 = r910080 - r910079;
        double r910095 = r910093 * r910094;
        double r910096 = r910092 + r910095;
        double r910097 = r910091 * r910084;
        double r910098 = r910090 ? r910096 : r910097;
        return r910098;
}

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

Original3.4
Target0.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- 1.0 (* (- 1.0 y) z)) < -2.3842446993784196e+131 or 6.033546520929353e+306 < (- 1.0 (* (- 1.0 y) z))

    1. Initial program 19.2

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

    3. Applied sub-neg19.2

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

    4. Applied distribute-lft-in19.2

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

    5. Simplified1.2

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

    if -2.3842446993784196e+131 < (- 1.0 (* (- 1.0 y) z)) < 6.033546520929353e+306

    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 simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \left(1 - y\right) \cdot z \le -2.3842446993784196 \cdot 10^{131} \lor \neg \left(1 - \left(1 - y\right) \cdot z \le 6.0335465209293531 \cdot 10^{306}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 +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))))