Average Error: 1.5 → 0.1
Time: 13.9s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1329896688031834:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\ \mathbf{elif}\;y \le 4.832848088860469210716999004498436556972 \cdot 10^{-23}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;y \le -1329896688031834:\\
\;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\

\mathbf{elif}\;y \le 4.832848088860469210716999004498436556972 \cdot 10^{-23}:\\
\;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r1292384 = x;
        double r1292385 = 4.0;
        double r1292386 = r1292384 + r1292385;
        double r1292387 = y;
        double r1292388 = r1292386 / r1292387;
        double r1292389 = r1292384 / r1292387;
        double r1292390 = z;
        double r1292391 = r1292389 * r1292390;
        double r1292392 = r1292388 - r1292391;
        double r1292393 = fabs(r1292392);
        return r1292393;
}
↓
double f(double x, double y, double z) {
        double r1292394 = y;
        double r1292395 = -1329896688031834.0;
        bool r1292396 = r1292394 <= r1292395;
        double r1292397 = x;
        double r1292398 = 4.0;
        double r1292399 = r1292397 + r1292398;
        double r1292400 = r1292399 / r1292394;
        double r1292401 = z;
        double r1292402 = r1292401 / r1292394;
        double r1292403 = r1292402 * r1292397;
        double r1292404 = r1292400 - r1292403;
        double r1292405 = fabs(r1292404);
        double r1292406 = 4.832848088860469e-23;
        bool r1292407 = r1292394 <= r1292406;
        double r1292408 = r1292397 * r1292401;
        double r1292409 = r1292399 - r1292408;
        double r1292410 = r1292409 / r1292394;
        double r1292411 = fabs(r1292410);
        double r1292412 = r1292407 ? r1292411 : r1292405;
        double r1292413 = r1292396 ? r1292405 : r1292412;
        return r1292413;
}

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 < -1329896688031834.0 or 4.832848088860469e-23 < y

    1. Initial program 2.5

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

    3. Applied div-inv2.5

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

    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 -1329896688031834.0 < y < 4.832848088860469e-23

    1. Initial program 0.1

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

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1329896688031834:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\ \mathbf{elif}\;y \le 4.832848088860469210716999004498436556972 \cdot 10^{-23}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))