Average Error: 3.3 → 0.3
Time: 2.8s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;1 - y \cdot z \le -5.7238574610871332 \cdot 10^{207} \lor \neg \left(1 - y \cdot z \le 4.14970720312397761 \cdot 10^{170}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(-y\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)\\ \end{array}\]
x \cdot \left(1 - y \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;1 - y \cdot z \le -5.7238574610871332 \cdot 10^{207} \lor \neg \left(1 - y \cdot z \le 4.14970720312397761 \cdot 10^{170}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot \left(-y\right)\right) \cdot z\\

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

\end{array}
double code(double x, double y, double z) {
	return ((double) (x * ((double) (1.0 - ((double) (y * z))))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((((double) (1.0 - ((double) (y * z)))) <= -5.723857461087133e+207) || !(((double) (1.0 - ((double) (y * z)))) <= 4.1497072031239776e+170))) {
		VAR = ((double) (((double) (x * 1.0)) + ((double) (((double) (x * ((double) -(y)))) * z))));
	} else {
		VAR = ((double) (((double) (x * ((double) (1.0 - ((double) (y * z)))))) + ((double) (x * ((double) fma(((double) -(z)), y, ((double) (z * y))))))));
	}
	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

Derivation

  1. Split input into 2 regimes

  2. if (- 1.0 (* y z)) < -5.723857461087133e+207 or 4.1497072031239776e+170 < (- 1.0 (* y z))

    1. Initial program 24.3

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

    3. Applied sub-neg24.3

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

    4. Applied distribute-lft-in24.3

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

    6. Applied distribute-lft-neg-in24.3

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

    7. Applied associate-*r*1.5

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

    if -5.723857461087133e+207 < (- 1.0 (* y z)) < 4.1497072031239776e+170

    1. Initial program 0.1

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

    3. Applied add-cube-cbrt0.1

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

    4. Applied prod-diff0.1

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

    5. Applied distribute-lft-in0.1

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

    6. Simplified0.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \le -5.7238574610871332 \cdot 10^{207} \lor \neg \left(1 - y \cdot z \le 4.14970720312397761 \cdot 10^{170}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(-y\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020123 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1 (* y z))))