Average Error: 3.4 → 0.2
Time: 2.1s
Precision: 64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \le -8.47236637384432409 \cdot 10^{252} \lor \neg \left(y \cdot z \le 1.02678798003438376 \cdot 10^{175}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(-y \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - y \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z \le -8.47236637384432409 \cdot 10^{252} \lor \neg \left(y \cdot z \le 1.02678798003438376 \cdot 10^{175}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(-y\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot 1 + x \cdot \left(-y \cdot z\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) (y * z)) <= -8.472366373844324e+252) || !(((double) (y * z)) <= 1.0267879800343838e+175))) {
		VAR = ((double) (((double) (x * 1.0)) + ((double) (((double) (x * z)) * ((double) -(y))))));
	} else {
		VAR = ((double) (((double) (x * 1.0)) + ((double) (x * ((double) -(((double) (y * z))))))));
	}
	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 (* y z) < -8.472366373844324e+252 or 1.0267879800343838e+175 < (* y z)

    1. Initial program 28.4

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

    3. Applied sub-neg28.4

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

    4. Applied distribute-lft-in28.4

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

    6. Applied *-commutative28.4

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

    7. Applied distribute-rgt-neg-in28.4

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

    8. Applied associate-*r*1.1

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

    if -8.472366373844324e+252 < (* y z) < 1.0267879800343838e+175

    1. Initial program 0.1

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

    3. Applied sub-neg0.1

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

    4. Applied distribute-lft-in0.1

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \le -8.47236637384432409 \cdot 10^{252} \lor \neg \left(y \cdot z \le 1.02678798003438376 \cdot 10^{175}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(-y \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020113 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1 (* y z))))