Average Error: 3.4 → 0.1
Time: 2.8s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.01904365721087831 \cdot 10^{54} \lor \neg \left(z \le 2.4536014589056785 \cdot 10^{-26}\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y - 1\right) + 1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 1, z, 1\right) \cdot x\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.01904365721087831 \cdot 10^{54} \lor \neg \left(z \le 2.4536014589056785 \cdot 10^{-26}\right):\\
\;\;\;\;\left(x \cdot z\right) \cdot \left(y - 1\right) + 1 \cdot x\\

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

\end{array}
double code(double x, double y, double z) {
	return (x * (1.0 - ((1.0 - y) * z)));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -4.019043657210878e+54) || !(z <= 2.4536014589056785e-26))) {
		VAR = (((x * z) * (y - 1.0)) + (1.0 * x));
	} else {
		VAR = (fma((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

Original3.4
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 < -4.019043657210878e+54 or 2.4536014589056785e-26 < z

    1. Initial program 9.1

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

    2. Simplified9.1

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

    4. Applied add-cube-cbrt10.1

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

    5. Taylor expanded around inf 9.1

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

    6. Simplified0.1

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

    8. Applied fma-udef0.1

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

    if -4.019043657210878e+54 < z < 2.4536014589056785e-26

    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 simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.01904365721087831 \cdot 10^{54} \lor \neg \left(z \le 2.4536014589056785 \cdot 10^{-26}\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y - 1\right) + 1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 1, z, 1\right) \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020075 +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))))