Average Error: 1.7 → 0.3
Time: 23.0s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -7.651634445924373 \cdot 10^{+46}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 2.3380013171410126 \cdot 10^{+66}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -7.651634445924373 \cdot 10^{+46}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{elif}\;x \le 2.3380013171410126 \cdot 10^{+66}:\\
\;\;\;\;\left|\frac{4 + x}{y} - \frac{z \cdot x}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r1082244 = x;
        double r1082245 = 4.0;
        double r1082246 = r1082244 + r1082245;
        double r1082247 = y;
        double r1082248 = r1082246 / r1082247;
        double r1082249 = r1082244 / r1082247;
        double r1082250 = z;
        double r1082251 = r1082249 * r1082250;
        double r1082252 = r1082248 - r1082251;
        double r1082253 = fabs(r1082252);
        return r1082253;
}
↓
double f(double x, double y, double z) {
        double r1082254 = x;
        double r1082255 = -7.651634445924373e+46;
        bool r1082256 = r1082254 <= r1082255;
        double r1082257 = 4.0;
        double r1082258 = r1082257 + r1082254;
        double r1082259 = y;
        double r1082260 = r1082258 / r1082259;
        double r1082261 = z;
        double r1082262 = r1082261 / r1082259;
        double r1082263 = r1082254 * r1082262;
        double r1082264 = r1082260 - r1082263;
        double r1082265 = fabs(r1082264);
        double r1082266 = 2.3380013171410126e+66;
        bool r1082267 = r1082254 <= r1082266;
        double r1082268 = r1082261 * r1082254;
        double r1082269 = r1082268 / r1082259;
        double r1082270 = r1082260 - r1082269;
        double r1082271 = fabs(r1082270);
        double r1082272 = r1082267 ? r1082271 : r1082265;
        double r1082273 = r1082256 ? r1082265 : r1082272;
        return r1082273;
}

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 < -7.651634445924373e+46 or 2.3380013171410126e+66 < x

    1. Initial program 0.1

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

    3. Applied div-inv0.2

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

    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 -7.651634445924373e+46 < x < 2.3380013171410126e+66

    1. Initial program 2.4

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

    3. Applied associate-*l/0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -7.651634445924373 \cdot 10^{+46}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 2.3380013171410126 \cdot 10^{+66}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))