Average Error: 1.6 → 0.1
Time: 1.8s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.12093481890030686 \lor \neg \left(x \le 1.662672792848544 \cdot 10^{36}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{-\left(\left(x + 4\right) - x \cdot z\right)}{-y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.12093481890030686 \lor \neg \left(x \le 1.662672792848544 \cdot 10^{36}\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{else}:\\
\;\;\;\;\left|\frac{-\left(\left(x + 4\right) - x \cdot z\right)}{-y}\right|\\

\end{array}
double code(double x, double y, double z) {
	return fabs((((x + 4.0) / y) - ((x / y) * z)));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((x <= -0.12093481890030686) || !(x <= 1.662672792848544e+36))) {
		VAR = fabs((((x + 4.0) / y) - (x * (z / y))));
	} else {
		VAR = fabs((-((x + 4.0) - (x * 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 x < -0.12093481890030686 or 1.662672792848544e+36 < x

    1. Initial program 0.1

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    2. Using strategy rm

    3. Applied div-inv0.2

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot z\right|\]

    4. Applied associate-*l*0.2

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \left(\frac{1}{y} \cdot z\right)}\right|\]

    5. Simplified0.1

      \[\leadsto \left|\frac{x + 4}{y} - x \cdot \color{blue}{\frac{z}{y}}\right|\]

    if -0.12093481890030686 < x < 1.662672792848544e+36

    1. Initial program 2.4

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    2. Using strategy rm

    3. Applied frac-2neg2.4

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{-x}{-y}} \cdot z\right|\]

    4. Applied associate-*l/0.1

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{\left(-x\right) \cdot z}{-y}}\right|\]

    5. Applied frac-2neg0.1

      \[\leadsto \left|\color{blue}{\frac{-\left(x + 4\right)}{-y}} - \frac{\left(-x\right) \cdot z}{-y}\right|\]

    6. Applied sub-div0.1

      \[\leadsto \left|\color{blue}{\frac{\left(-\left(x + 4\right)\right) - \left(-x\right) \cdot z}{-y}}\right|\]

    7. Simplified0.1

      \[\leadsto \left|\frac{\color{blue}{-\left(\left(x + 4\right) - x \cdot z\right)}}{-y}\right|\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.12093481890030686 \lor \neg \left(x \le 1.662672792848544 \cdot 10^{36}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{-\left(\left(x + 4\right) - x \cdot z\right)}{-y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020071 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))