Average Error: 1.5 → 0.8
Time: 3.6s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.032765563446886112648138640997485857612 \cdot 10^{47}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right) + 4 \cdot \frac{1}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.032765563446886112648138640997485857612 \cdot 10^{47}:\\
\;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{else}:\\
\;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right) + 4 \cdot \frac{1}{y}\right|\\

\end{array}
double f(double x, double y, double z) {
        double r28357 = x;
        double r28358 = 4.0;
        double r28359 = r28357 + r28358;
        double r28360 = y;
        double r28361 = r28359 / r28360;
        double r28362 = r28357 / r28360;
        double r28363 = z;
        double r28364 = r28362 * r28363;
        double r28365 = r28361 - r28364;
        double r28366 = fabs(r28365);
        return r28366;
}
↓
double f(double x, double y, double z) {
        double r28367 = y;
        double r28368 = -1.0327655634468861e+47;
        bool r28369 = r28367 <= r28368;
        double r28370 = x;
        double r28371 = 4.0;
        double r28372 = r28370 + r28371;
        double r28373 = r28372 / r28367;
        double r28374 = z;
        double r28375 = r28374 / r28367;
        double r28376 = r28370 * r28375;
        double r28377 = r28373 - r28376;
        double r28378 = fabs(r28377);
        double r28379 = r28370 / r28367;
        double r28380 = 1.0;
        double r28381 = r28380 - r28374;
        double r28382 = r28379 * r28381;
        double r28383 = r28380 / r28367;
        double r28384 = r28371 * r28383;
        double r28385 = r28382 + r28384;
        double r28386 = fabs(r28385);
        double r28387 = r28369 ? r28378 : r28386;
        return r28387;
}

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 y < -1.0327655634468861e+47

    1. Initial program 2.9

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

    3. Applied div-inv2.9

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

    4. Applied associate-*l*0.1

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

    5. Simplified0.1

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

    if -1.0327655634468861e+47 < y

    1. Initial program 1.0

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

    2. Taylor expanded around 0 2.5

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

    3. Simplified1.0

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.032765563446886112648138640997485857612 \cdot 10^{47}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right) + 4 \cdot \frac{1}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))