Average Error: 1.7 → 0.1
Time: 3.5s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1097352739.18932986 \lor \neg \left(x \le 1.1704247077394178 \cdot 10^{-39}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -1097352739.18932986 \lor \neg \left(x \le 1.1704247077394178 \cdot 10^{-39}\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\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 r29028 = x;
        double r29029 = 4.0;
        double r29030 = r29028 + r29029;
        double r29031 = y;
        double r29032 = r29030 / r29031;
        double r29033 = r29028 / r29031;
        double r29034 = z;
        double r29035 = r29033 * r29034;
        double r29036 = r29032 - r29035;
        double r29037 = fabs(r29036);
        return r29037;
}
↓
double f(double x, double y, double z) {
        double r29038 = x;
        double r29039 = -1097352739.1893299;
        bool r29040 = r29038 <= r29039;
        double r29041 = 1.1704247077394178e-39;
        bool r29042 = r29038 <= r29041;
        double r29043 = !r29042;
        bool r29044 = r29040 || r29043;
        double r29045 = 4.0;
        double r29046 = r29038 + r29045;
        double r29047 = y;
        double r29048 = r29046 / r29047;
        double r29049 = r29038 / r29047;
        double r29050 = z;
        double r29051 = r29049 * r29050;
        double r29052 = r29048 - r29051;
        double r29053 = fabs(r29052);
        double r29054 = r29038 * r29050;
        double r29055 = r29046 - r29054;
        double r29056 = r29055 / r29047;
        double r29057 = fabs(r29056);
        double r29058 = r29044 ? r29053 : r29057;
        return r29058;
}

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 < -1097352739.1893299 or 1.1704247077394178e-39 < x

    1. Initial program 0.2

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

    if -1097352739.1893299 < x < 1.1704247077394178e-39

    1. Initial program 2.8

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

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1097352739.18932986 \lor \neg \left(x \le 1.1704247077394178 \cdot 10^{-39}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))