Average Error: 3.6 → 0.3
Time: 3.1s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.0430726878723873 \cdot 10^{-22} \lor \neg \left(z \le 1.41338966371794329 \cdot 10^{-113}\right):\\ \;\;\;\;\mathsf{fma}\left(x \cdot z, y - 1, 1 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 1, z, 1\right) \cdot x\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.0430726878723873 \cdot 10^{-22} \lor \neg \left(z \le 1.41338966371794329 \cdot 10^{-113}\right):\\
\;\;\;\;\mathsf{fma}\left(x \cdot z, y - 1, 1 \cdot x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y - 1, z, 1\right) \cdot x\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (x * ((double) (1.0 - ((double) (((double) (1.0 - y)) * z))))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -1.0430726878723873e-22) || !(z <= 1.4133896637179433e-113))) {
		VAR = ((double) fma(((double) (x * z)), ((double) (y - 1.0)), ((double) (1.0 * x))));
	} else {
		VAR = ((double) (((double) fma(((double) (y - 1.0)), z, 1.0)) * x));
	}
	return VAR;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -1.0430726878723873e-22 or 1.4133896637179433e-113 < z

    1. Initial program 6.8

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]

    2. Simplified6.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 1, z, 1\right) \cdot x}\]
    3. Using strategy rm

    4. Applied add-cube-cbrt7.7

      \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(y - 1, z, 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(y - 1, z, 1\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(y - 1, z, 1\right)}\right)} \cdot x\]

    5. Taylor expanded around inf 6.8

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

    6. Simplified0.5

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

    if -1.0430726878723873e-22 < z < 1.4133896637179433e-113

    1. Initial program 0.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]

    2. Simplified0.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 1, z, 1\right) \cdot x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.0430726878723873 \cdot 10^{-22} \lor \neg \left(z \le 1.41338966371794329 \cdot 10^{-113}\right):\\ \;\;\;\;\mathsf{fma}\left(x \cdot z, y - 1, 1 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 1, z, 1\right) \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020122 +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))))