Average Error: 3.3 → 1.9
Time: 3.3s
Precision: binary64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -2.7737198986946373 \cdot 10^{+183}:\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array}\]
x \cdot \left(1 - y \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z \leq -2.7737198986946373 \cdot 10^{+183}:\\
\;\;\;\;x - z \cdot \left(y \cdot x\right)\\

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

\end{array}
(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -2.7737198986946373e+183)
   (- x (* z (* y x)))
   (- x (* (* y z) x))))
double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -2.7737198986946373e+183) {
		tmp = x - (z * (y * x));
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

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 (*.f64 y z) < -2.7737198986946373e183

    1. Initial program 22.2

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

    3. Applied sub-neg_binary64_1030122.2

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

    4. Applied distribute-rgt-in_binary64_1025822.2

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

    5. Simplified22.2

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

    6. Simplified22.2

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

    8. Applied distribute-rgt-neg-in_binary64_1026622.2

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

    9. Applied associate-*r*_binary64_102482.3

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

    if -2.7737198986946373e183 < (*.f64 y z)

    1. Initial program 1.9

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

    3. Applied sub-neg_binary64_103011.9

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

    4. Applied distribute-rgt-in_binary64_102581.9

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

    5. Simplified1.9

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

    6. Simplified1.9

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

    8. Applied distribute-rgt-neg-out_binary64_102681.9

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

    9. Applied unsub-neg_binary64_103021.9

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2.7737198986946373 \cdot 10^{+183}:\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020344 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))