Average Error: 1.7 → 0.5
Time: 2.2s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.60547792176699934 \cdot 10^{-42} \lor \neg \left(x \le 3.1150961226047512 \cdot 10^{-144}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{1}{\frac{y}{\left(x + 4\right) - x \cdot z}}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.60547792176699934 \cdot 10^{-42} \lor \neg \left(x \le 3.1150961226047512 \cdot 10^{-144}\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{else}:\\
\;\;\;\;\left|\frac{1}{\frac{y}{\left(x + 4\right) - x \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 (((x <= -2.6054779217669993e-42) || !(x <= 3.115096122604751e-144))) {
		VAR = ((double) fabs(((double) (((double) (((double) (x + 4.0)) / y)) - ((double) (x * ((double) (z / y))))))));
	} else {
		VAR = ((double) fabs(((double) (1.0 / ((double) (y / ((double) (((double) (x + 4.0)) - ((double) (x * 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 x < -2.6054779217669993e-42 or 3.115096122604751e-144 < x

    1. Initial program 0.7

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

    3. Applied div-inv0.8

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

    4. Applied associate-*l*0.9

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

    5. Simplified0.9

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

    if -2.6054779217669993e-42 < x < 3.115096122604751e-144

    1. Initial program 3.0

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

      \[\leadsto \left|\color{blue}{\frac{1}{\frac{y}{\left(x + 4\right) - x \cdot z}}}\right|\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.60547792176699934 \cdot 10^{-42} \lor \neg \left(x \le 3.1150961226047512 \cdot 10^{-144}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{1}{\frac{y}{\left(x + 4\right) - x \cdot z}}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020121 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))