Average Error: 1.6 → 1.5
Time: 14.4s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.492066452799628 \cdot 10^{+60}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.492066452799628 \cdot 10^{+60}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r963454 = x;
        double r963455 = 4.0;
        double r963456 = r963454 + r963455;
        double r963457 = y;
        double r963458 = r963456 / r963457;
        double r963459 = r963454 / r963457;
        double r963460 = z;
        double r963461 = r963459 * r963460;
        double r963462 = r963458 - r963461;
        double r963463 = fabs(r963462);
        return r963463;
}
↓
double f(double x, double y, double z) {
        double r963464 = x;
        double r963465 = -1.492066452799628e+60;
        bool r963466 = r963464 <= r963465;
        double r963467 = 4.0;
        double r963468 = r963467 + r963464;
        double r963469 = y;
        double r963470 = r963468 / r963469;
        double r963471 = z;
        double r963472 = r963471 / r963469;
        double r963473 = r963464 * r963472;
        double r963474 = r963470 - r963473;
        double r963475 = fabs(r963474);
        double r963476 = r963471 * r963464;
        double r963477 = r963468 - r963476;
        double r963478 = r963477 / r963469;
        double r963479 = fabs(r963478);
        double r963480 = r963466 ? r963475 : r963479;
        return r963480;
}

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 < -1.492066452799628e+60

    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 -1.492066452799628e+60 < x

    1. Initial program 1.9

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

    3. Applied associate-*l/1.7

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

    4. Applied sub-div1.7

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.492066452799628 \cdot 10^{+60}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))