Average Error: 3.6 → 0.2
Time: 3.9s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -2.80631460883752581 \cdot 10^{-74} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 1.33855618048273198 \cdot 10^{133}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -2.80631460883752581 \cdot 10^{-74} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 1.33855618048273198 \cdot 10^{133}\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 r796136 = x;
        double r796137 = 1.0;
        double r796138 = y;
        double r796139 = r796137 - r796138;
        double r796140 = z;
        double r796141 = r796139 * r796140;
        double r796142 = r796137 - r796141;
        double r796143 = r796136 * r796142;
        return r796143;
}
↓
double f(double x, double y, double z) {
        double r796144 = x;
        double r796145 = 1.0;
        double r796146 = y;
        double r796147 = r796145 - r796146;
        double r796148 = z;
        double r796149 = r796147 * r796148;
        double r796150 = r796145 - r796149;
        double r796151 = r796144 * r796150;
        double r796152 = -2.806314608837526e-74;
        bool r796153 = r796151 <= r796152;
        double r796154 = 1.338556180482732e+133;
        bool r796155 = r796151 <= r796154;
        double r796156 = !r796155;
        bool r796157 = r796153 || r796156;
        double r796158 = r796144 * r796145;
        double r796159 = r796144 * r796148;
        double r796160 = r796146 - r796145;
        double r796161 = r796159 * r796160;
        double r796162 = r796158 + r796161;
        double r796163 = r796148 * r796146;
        double r796164 = r796144 * r796163;
        double r796165 = -r796145;
        double r796166 = r796159 * r796165;
        double r796167 = r796164 + r796166;
        double r796168 = r796158 + r796167;
        double r796169 = r796157 ? r796162 : r796168;
        return r796169;
}

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

Original3.6
Target0.2
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 (* x (- 1.0 (* (- 1.0 y) z))) < -2.806314608837526e-74 or 1.338556180482732e+133 < (* x (- 1.0 (* (- 1.0 y) z)))

    1. Initial program 6.6

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

    3. Applied sub-neg6.6

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

    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 -2.806314608837526e-74 < (* x (- 1.0 (* (- 1.0 y) z))) < 1.338556180482732e+133

    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. Simplified3.5

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

    7. Applied sub-neg3.5

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

    8. Applied distribute-lft-in3.5

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

    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le -2.80631460883752581 \cdot 10^{-74} \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 1.33855618048273198 \cdot 10^{133}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))))