Average Error: 1.6 → 1.5
Time: 15.1s
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 r862234 = x;
        double r862235 = 4.0;
        double r862236 = r862234 + r862235;
        double r862237 = y;
        double r862238 = r862236 / r862237;
        double r862239 = r862234 / r862237;
        double r862240 = z;
        double r862241 = r862239 * r862240;
        double r862242 = r862238 - r862241;
        double r862243 = fabs(r862242);
        return r862243;
}
↓
double f(double x, double y, double z) {
        double r862244 = x;
        double r862245 = -1.492066452799628e+60;
        bool r862246 = r862244 <= r862245;
        double r862247 = 4.0;
        double r862248 = r862247 + r862244;
        double r862249 = y;
        double r862250 = r862248 / r862249;
        double r862251 = z;
        double r862252 = r862251 / r862249;
        double r862253 = r862244 * r862252;
        double r862254 = r862250 - r862253;
        double r862255 = fabs(r862254);
        double r862256 = r862251 * r862244;
        double r862257 = r862248 - r862256;
        double r862258 = r862257 / r862249;
        double r862259 = fabs(r862258);
        double r862260 = r862246 ? r862255 : r862259;
        return r862260;
}

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