Average Error: 1.9 → 0.1
Time: 10.1s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.177271937169595483422970684993734880398 \cdot 10^{-17} \lor \neg \left(x \le 3.980546299544918028958510427590163807717 \cdot 10^{-38}\right):\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{\frac{y}{z}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(4 - z \cdot x\right) + x}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.177271937169595483422970684993734880398 \cdot 10^{-17} \lor \neg \left(x \le 3.980546299544918028958510427590163807717 \cdot 10^{-38}\right):\\
\;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{\frac{y}{z}}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r25290 = x;
        double r25291 = 4.0;
        double r25292 = r25290 + r25291;
        double r25293 = y;
        double r25294 = r25292 / r25293;
        double r25295 = r25290 / r25293;
        double r25296 = z;
        double r25297 = r25295 * r25296;
        double r25298 = r25294 - r25297;
        double r25299 = fabs(r25298);
        return r25299;
}
↓
double f(double x, double y, double z) {
        double r25300 = x;
        double r25301 = -1.1772719371695955e-17;
        bool r25302 = r25300 <= r25301;
        double r25303 = 3.980546299544918e-38;
        bool r25304 = r25300 <= r25303;
        double r25305 = !r25304;
        bool r25306 = r25302 || r25305;
        double r25307 = 4.0;
        double r25308 = r25307 + r25300;
        double r25309 = y;
        double r25310 = r25308 / r25309;
        double r25311 = z;
        double r25312 = r25309 / r25311;
        double r25313 = r25300 / r25312;
        double r25314 = r25310 - r25313;
        double r25315 = fabs(r25314);
        double r25316 = r25311 * r25300;
        double r25317 = r25307 - r25316;
        double r25318 = r25317 + r25300;
        double r25319 = r25318 / r25309;
        double r25320 = fabs(r25319);
        double r25321 = r25306 ? r25315 : r25320;
        return r25321;
}

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 < -1.1772719371695955e-17 or 3.980546299544918e-38 < x

    1. Initial program 0.2

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

    2. Taylor expanded around 0 8.8

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

    3. Simplified0.2

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

    4. Taylor expanded around 0 8.8

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

    5. Simplified0.2

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

    if -1.1772719371695955e-17 < x < 3.980546299544918e-38

    1. Initial program 3.3

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    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. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.177271937169595483422970684993734880398 \cdot 10^{-17} \lor \neg \left(x \le 3.980546299544918028958510427590163807717 \cdot 10^{-38}\right):\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{\frac{y}{z}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(4 - z \cdot x\right) + x}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))