Average Error: 1.4 → 0.4
Time: 11.7s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.1618774464985056 \cdot 10^{+63}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \le 3.5037736689937804 \cdot 10^{-122}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.1618774464985056 \cdot 10^{+63}:\\
\;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\

\mathbf{elif}\;x \le 3.5037736689937804 \cdot 10^{-122}:\\
\;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r491039 = x;
        double r491040 = 4.0;
        double r491041 = r491039 + r491040;
        double r491042 = y;
        double r491043 = r491041 / r491042;
        double r491044 = r491039 / r491042;
        double r491045 = z;
        double r491046 = r491044 * r491045;
        double r491047 = r491043 - r491046;
        double r491048 = fabs(r491047);
        return r491048;
}
↓
double f(double x, double y, double z) {
        double r491049 = x;
        double r491050 = -2.1618774464985056e+63;
        bool r491051 = r491049 <= r491050;
        double r491052 = 4.0;
        double r491053 = r491052 + r491049;
        double r491054 = y;
        double r491055 = r491053 / r491054;
        double r491056 = r491049 / r491054;
        double r491057 = z;
        double r491058 = r491056 * r491057;
        double r491059 = r491055 - r491058;
        double r491060 = fabs(r491059);
        double r491061 = 3.5037736689937804e-122;
        bool r491062 = r491049 <= r491061;
        double r491063 = r491049 * r491057;
        double r491064 = r491053 - r491063;
        double r491065 = r491064 / r491054;
        double r491066 = fabs(r491065);
        double r491067 = r491062 ? r491066 : r491060;
        double r491068 = r491051 ? r491060 : r491067;
        return r491068;
}

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 < -2.1618774464985056e+63 or 3.5037736689937804e-122 < x

    1. Initial program 0.4

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

    if -2.1618774464985056e+63 < x < 3.5037736689937804e-122

    1. Initial program 2.3

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

    3. Applied associate-*l/0.3

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

    4. Applied sub-div0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.1618774464985056 \cdot 10^{+63}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \le 3.5037736689937804 \cdot 10^{-122}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019152 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))