Average Error: 3.5 → 0.1
Time: 2.8s
Precision: binary64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2.667397886615548 \cdot 10^{+300}\right):\\ \;\;\;\;x \cdot 1 - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 - \left(y \cdot z\right) \cdot x\\ \end{array}\]
x \cdot \left(1 - y \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2.667397886615548 \cdot 10^{+300}\right):\\
\;\;\;\;x \cdot 1 - z \cdot \left(y \cdot x\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot 1 - \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) (- INFINITY)) (not (<= (* y z) 2.667397886615548e+300)))
   (- (* x 1.0) (* z (* y x)))
   (- (* x 1.0) (* (* y z) x))))
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 tmp;
	if (((((double) (y * z)) <= ((double) -(((double) INFINITY)))) || !(((double) (y * z)) <= 2.667397886615548e+300))) {
		tmp = ((double) (((double) (x * 1.0)) - ((double) (z * ((double) (y * x))))));
	} else {
		tmp = ((double) (((double) (x * 1.0)) - ((double) (((double) (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 (* y z) < -inf.0 or 2.6673978866155481e300 < (* y z)

    1. Initial program Error: 61.1 bits

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

    3. Applied sub-negError: 61.1 bits

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

    4. Applied distribute-lft-inError: 61.1 bits

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

    5. SimplifiedError: 61.1 bits

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

    7. Applied associate-*r*Error: 0.2 bits

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

    if -inf.0 < (* y z) < 2.6673978866155481e300

    1. Initial program Error: 0.1 bits

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

    3. Applied sub-negError: 0.1 bits

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

    4. Applied distribute-lft-inError: 0.1 bits

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

    5. SimplifiedError: 0.1 bits

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

  4. Final simplificationError: 0.1 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2.667397886615548 \cdot 10^{+300}\right):\\ \;\;\;\;x \cdot 1 - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 - \left(y \cdot z\right) \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))