Average Error: 3.4 → 0.1
Time: 2.9s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -4.2964364808141009 \cdot 10^{174} \lor \neg \left(\left(1 - y\right) \cdot z \le 2.9196113773829551 \cdot 10^{253}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(1 - y\right) \cdot z \le -4.2964364808141009 \cdot 10^{174} \lor \neg \left(\left(1 - y\right) \cdot z \le 2.9196113773829551 \cdot 10^{253}\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 r772517 = x;
        double r772518 = 1.0;
        double r772519 = y;
        double r772520 = r772518 - r772519;
        double r772521 = z;
        double r772522 = r772520 * r772521;
        double r772523 = r772518 - r772522;
        double r772524 = r772517 * r772523;
        return r772524;
}
↓
double f(double x, double y, double z) {
        double r772525 = 1.0;
        double r772526 = y;
        double r772527 = r772525 - r772526;
        double r772528 = z;
        double r772529 = r772527 * r772528;
        double r772530 = -4.296436480814101e+174;
        bool r772531 = r772529 <= r772530;
        double r772532 = 2.919611377382955e+253;
        bool r772533 = r772529 <= r772532;
        double r772534 = !r772533;
        bool r772535 = r772531 || r772534;
        double r772536 = x;
        double r772537 = r772536 * r772525;
        double r772538 = r772536 * r772528;
        double r772539 = r772526 - r772525;
        double r772540 = r772538 * r772539;
        double r772541 = r772537 + r772540;
        double r772542 = r772528 * r772526;
        double r772543 = r772536 * r772542;
        double r772544 = -r772525;
        double r772545 = r772538 * r772544;
        double r772546 = r772543 + r772545;
        double r772547 = r772537 + r772546;
        double r772548 = r772535 ? r772541 : r772547;
        return r772548;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (* (- 1.0 y) z) < -4.296436480814101e+174 or 2.919611377382955e+253 < (* (- 1.0 y) z)

    1. Initial program 21.3

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

    3. Applied sub-neg21.3

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

    4. Applied distribute-lft-in21.3

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

    5. Simplified0.5

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

    if -4.296436480814101e+174 < (* (- 1.0 y) z) < 2.919611377382955e+253

    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. Simplified1.8

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

    7. Applied sub-neg1.8

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

    8. Applied distribute-lft-in1.8

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

    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 simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -4.2964364808141009 \cdot 10^{174} \lor \neg \left(\left(1 - y\right) \cdot z \le 2.9196113773829551 \cdot 10^{253}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(z \cdot y\right) + \left(x \cdot z\right) \cdot \left(-1\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))))