Average Error: 1.7 → 0.6
Time: 13.8s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.05718793893972162 \cdot 10^{142} \lor \neg \left(x \le 8.6806295500210938 \cdot 10^{-56}\right):\\ \;\;\;\;\left|\frac{4}{y} + \frac{x}{y} \cdot \left(1 - z\right)\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.05718793893972162 \cdot 10^{142} \lor \neg \left(x \le 8.6806295500210938 \cdot 10^{-56}\right):\\
\;\;\;\;\left|\frac{4}{y} + \frac{x}{y} \cdot \left(1 - z\right)\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 r28077 = x;
        double r28078 = 4.0;
        double r28079 = r28077 + r28078;
        double r28080 = y;
        double r28081 = r28079 / r28080;
        double r28082 = r28077 / r28080;
        double r28083 = z;
        double r28084 = r28082 * r28083;
        double r28085 = r28081 - r28084;
        double r28086 = fabs(r28085);
        return r28086;
}
↓
double f(double x, double y, double z) {
        double r28087 = x;
        double r28088 = -2.0571879389397216e+142;
        bool r28089 = r28087 <= r28088;
        double r28090 = 8.680629550021094e-56;
        bool r28091 = r28087 <= r28090;
        double r28092 = !r28091;
        bool r28093 = r28089 || r28092;
        double r28094 = 4.0;
        double r28095 = y;
        double r28096 = r28094 / r28095;
        double r28097 = r28087 / r28095;
        double r28098 = 1.0;
        double r28099 = z;
        double r28100 = r28098 - r28099;
        double r28101 = r28097 * r28100;
        double r28102 = r28096 + r28101;
        double r28103 = fabs(r28102);
        double r28104 = r28087 + r28094;
        double r28105 = r28087 * r28099;
        double r28106 = r28104 - r28105;
        double r28107 = r28106 / r28095;
        double r28108 = fabs(r28107);
        double r28109 = r28093 ? r28103 : r28108;
        return r28109;
}

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 < -2.0571879389397216e+142 or 8.680629550021094e-56 < x

    1. Initial program 0.3

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

    2. Taylor expanded around 0 9.2

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

    3. Simplified0.3

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

    if -2.0571879389397216e+142 < x < 8.680629550021094e-56

    1. Initial program 2.5

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

    3. Applied associate-*l/0.8

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

    4. Applied sub-div0.7

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.05718793893972162 \cdot 10^{142} \lor \neg \left(x \le 8.6806295500210938 \cdot 10^{-56}\right):\\ \;\;\;\;\left|\frac{4}{y} + \frac{x}{y} \cdot \left(1 - z\right)\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))