Average Error: 3.3 → 0.4
Time: 3.0s
Precision: binary64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.8262304376441536 \cdot 10^{+140} \lor \neg \left(y \cdot z \leq 6.825761707952501 \cdot 10^{+210}\right):\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array}\]
x \cdot \left(1 - y \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z \leq -1.8262304376441536 \cdot 10^{+140} \lor \neg \left(y \cdot z \leq 6.825761707952501 \cdot 10^{+210}\right):\\
\;\;\;\;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 (or (<= (* y z) -1.8262304376441536e+140)
         (not (<= (* y z) 6.825761707952501e+210)))
   (- 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) <= -1.8262304376441536e+140) || !((y * z) <= 6.825761707952501e+210)) {
		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) < -1.8262304376441536e140 or 6.8257617079525008e210 < (*.f64 y z)

    1. Initial program 21.7

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

    3. Applied sub-neg_binary64_1108021.7

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

    4. Applied distribute-rgt-in_binary64_1103721.7

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

    5. Simplified21.7

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

    6. Simplified21.7

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

    8. Applied distribute-rgt-neg-in_binary64_1104521.7

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

    9. Applied associate-*r*_binary64_110272.1

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

    if -1.8262304376441536e140 < (*.f64 y z) < 6.8257617079525008e210

    1. Initial program 0.1

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

    3. Applied sub-neg_binary64_110800.1

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

    4. Applied distribute-rgt-in_binary64_110370.1

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

    5. Simplified0.1

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

    6. Simplified0.1

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.8262304376441536 \cdot 10^{+140} \lor \neg \left(y \cdot z \leq 6.825761707952501 \cdot 10^{+210}\right):\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020281 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))