Average Error: 3.5 → 0.1
Time: 3.7s
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 r807509 = x;
        double r807510 = 1.0;
        double r807511 = y;
        double r807512 = r807510 - r807511;
        double r807513 = z;
        double r807514 = r807512 * r807513;
        double r807515 = r807510 - r807514;
        double r807516 = r807509 * r807515;
        return r807516;
}
↓
double f(double x, double y, double z) {
        double r807517 = z;
        double r807518 = -5.963481389703192e-17;
        bool r807519 = r807517 <= r807518;
        double r807520 = 1.102656055982303e-48;
        bool r807521 = r807517 <= r807520;
        double r807522 = !r807521;
        bool r807523 = r807519 || r807522;
        double r807524 = x;
        double r807525 = 1.0;
        double r807526 = r807524 * r807525;
        double r807527 = r807524 * r807517;
        double r807528 = y;
        double r807529 = r807528 - r807525;
        double r807530 = r807527 * r807529;
        double r807531 = r807526 + r807530;
        double r807532 = r807525 - r807528;
        double r807533 = r807532 * r807517;
        double r807534 = r807525 - r807533;
        double r807535 = r807524 * r807534;
        double r807536 = r807523 ? r807531 : r807535;
        return r807536;
}

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 
(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))))