Average Error: 1.3 → 0.1
Time: 3.5s
Precision: binary64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x + 4}{y} - \frac{x}{y} \cdot z \leq -7.617708137011477 \cdot 10^{+34} \lor \neg \left(\frac{x + 4}{y} - \frac{x}{y} \cdot z \leq 2.622117664153231 \cdot 10^{-63}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;\frac{x + 4}{y} - \frac{x}{y} \cdot z \leq -7.617708137011477 \cdot 10^{+34} \lor \neg \left(\frac{x + 4}{y} - \frac{x}{y} \cdot z \leq 2.622117664153231 \cdot 10^{-63}\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\

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

\end{array}
(FPCore (x y z) :precision binary64 (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= (- (/ (+ x 4.0) y) (* (/ x y) z)) -7.617708137011477e+34)
         (not (<= (- (/ (+ x 4.0) y) (* (/ x y) z)) 2.622117664153231e-63)))
   (fabs (- (/ (+ x 4.0) y) (* (/ x y) z)))
   (fabs (/ (- (+ x 4.0) (* x z)) y))))
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 tmp;
	if (((((x + 4.0) / y) - ((x / y) * z)) <= -7.617708137011477e+34) || !((((x + 4.0) / y) - ((x / y) * z)) <= 2.622117664153231e-63)) {
		tmp = fabs(((x + 4.0) / y) - ((x / y) * z));
	} else {
		tmp = fabs(((x + 4.0) - (x * z)) / y);
	}
	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 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)) < -7.617708137011477e34 or 2.622117664153231e-63 < (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))

    1. Initial program 0.1

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

    if -7.617708137011477e34 < (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)) < 2.622117664153231e-63

    1. Initial program 3.5

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

    2. Simplified0.2

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + 4}{y} - \frac{x}{y} \cdot z \leq -7.617708137011477 \cdot 10^{+34} \lor \neg \left(\frac{x + 4}{y} - \frac{x}{y} \cdot z \leq 2.622117664153231 \cdot 10^{-63}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020295 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))