Average Error: 1.6 → 0.1
Time: 9.4s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.4899595848850141 \cdot 10^{46} \lor \neg \left(x \le 2.0322004459479788 \cdot 10^{-8}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.4899595848850141 \cdot 10^{46} \lor \neg \left(x \le 2.0322004459479788 \cdot 10^{-8}\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r30326 = x;
        double r30327 = 4.0;
        double r30328 = r30326 + r30327;
        double r30329 = y;
        double r30330 = r30328 / r30329;
        double r30331 = r30326 / r30329;
        double r30332 = z;
        double r30333 = r30331 * r30332;
        double r30334 = r30330 - r30333;
        double r30335 = fabs(r30334);
        return r30335;
}
↓
double f(double x, double y, double z) {
        double r30336 = x;
        double r30337 = -1.489959584885014e+46;
        bool r30338 = r30336 <= r30337;
        double r30339 = 2.0322004459479788e-08;
        bool r30340 = r30336 <= r30339;
        double r30341 = !r30340;
        bool r30342 = r30338 || r30341;
        double r30343 = 4.0;
        double r30344 = r30336 + r30343;
        double r30345 = y;
        double r30346 = r30344 / r30345;
        double r30347 = z;
        double r30348 = r30347 / r30345;
        double r30349 = r30336 * r30348;
        double r30350 = r30346 - r30349;
        double r30351 = fabs(r30350);
        double r30352 = r30336 * r30347;
        double r30353 = r30344 - r30352;
        double r30354 = r30353 / r30345;
        double r30355 = fabs(r30354);
        double r30356 = r30342 ? r30351 : r30355;
        return r30356;
}

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 < -1.489959584885014e+46 or 2.0322004459479788e-08 < 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*0.2

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

    5. Simplified0.1

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

    if -1.489959584885014e+46 < x < 2.0322004459479788e-08

    1. Initial program 2.4

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

    3. Applied associate-*l/0.2

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

    4. Applied sub-div0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.4899595848850141 \cdot 10^{46} \lor \neg \left(x \le 2.0322004459479788 \cdot 10^{-8}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))