Average Error: 1.7 → 0.5
Time: 2.9s
Precision: binary64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \le 1.5534752070982489 \cdot 10^{-194}:\\ \;\;\;\;\left|\frac{1}{\frac{y}{\left(x + 4\right) - x \cdot z}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \le 1.5534752070982489 \cdot 10^{-194}:\\
\;\;\;\;\left|\frac{1}{\frac{y}{\left(x + 4\right) - x \cdot z}}\right|\\

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

\end{array}
double code(double x, double y, double z) {
	return ((double) fabs(((double) (((double) (((double) (x + 4.0)) / y)) - ((double) (((double) (x / y)) * z))))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((((double) fabs(((double) (((double) (((double) (x + 4.0)) / y)) - ((double) (((double) (x / y)) * z)))))) <= 1.553475207098249e-194)) {
		VAR = ((double) fabs(((double) (1.0 / ((double) (y / ((double) (((double) (x + 4.0)) - ((double) (x * z))))))))));
	} else {
		VAR = ((double) fabs(((double) (((double) (((double) (x + 4.0)) / y)) - ((double) (((double) (x / 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 (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))) < 1.5534752070982489e-194

    1. Initial program 9.5

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

    3. Applied associate-*l/0.1

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

    4. Applied sub-div0.1

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

    6. Applied clear-num0.1

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

    if 1.5534752070982489e-194 < (fabs (- (/ (+ x 4.0) y) (* (/ x y) z)))

    1. Initial program 0.6

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \le 1.5534752070982489 \cdot 10^{-194}:\\ \;\;\;\;\left|\frac{1}{\frac{y}{\left(x + 4\right) - x \cdot z}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020161 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))