Average Error: 3.4 → 0.3
Time: 3.4s
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 r967205 = x;
        double r967206 = 1.0;
        double r967207 = y;
        double r967208 = r967206 - r967207;
        double r967209 = z;
        double r967210 = r967208 * r967209;
        double r967211 = r967206 - r967210;
        double r967212 = r967205 * r967211;
        return r967212;
}
↓
double f(double x, double y, double z) {
        double r967213 = 1.0;
        double r967214 = y;
        double r967215 = r967213 - r967214;
        double r967216 = z;
        double r967217 = r967215 * r967216;
        double r967218 = r967213 - r967217;
        double r967219 = -2.3842446993784196e+131;
        bool r967220 = r967218 <= r967219;
        double r967221 = 6.033546520929353e+306;
        bool r967222 = r967218 <= r967221;
        double r967223 = !r967222;
        bool r967224 = r967220 || r967223;
        double r967225 = x;
        double r967226 = r967225 * r967213;
        double r967227 = r967225 * r967216;
        double r967228 = r967214 - r967213;
        double r967229 = r967227 * r967228;
        double r967230 = r967226 + r967229;
        double r967231 = r967225 * r967218;
        double r967232 = r967224 ? r967230 : r967231;
        return r967232;
}

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 
(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))))