Average Error: 1.7 → 0.3
Time: 17.1s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.885444965291613 \cdot 10^{+46}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 1.0213139804930134 \cdot 10^{+68}:\\ \;\;\;\;\left|\frac{4}{y} + \frac{x - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -6.885444965291613 \cdot 10^{+46}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{elif}\;x \le 1.0213139804930134 \cdot 10^{+68}:\\
\;\;\;\;\left|\frac{4}{y} + \frac{x - z \cdot x}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r1261946 = x;
        double r1261947 = 4.0;
        double r1261948 = r1261946 + r1261947;
        double r1261949 = y;
        double r1261950 = r1261948 / r1261949;
        double r1261951 = r1261946 / r1261949;
        double r1261952 = z;
        double r1261953 = r1261951 * r1261952;
        double r1261954 = r1261950 - r1261953;
        double r1261955 = fabs(r1261954);
        return r1261955;
}
↓
double f(double x, double y, double z) {
        double r1261956 = x;
        double r1261957 = -6.885444965291613e+46;
        bool r1261958 = r1261956 <= r1261957;
        double r1261959 = 4.0;
        double r1261960 = r1261959 + r1261956;
        double r1261961 = y;
        double r1261962 = r1261960 / r1261961;
        double r1261963 = z;
        double r1261964 = r1261963 / r1261961;
        double r1261965 = r1261956 * r1261964;
        double r1261966 = r1261962 - r1261965;
        double r1261967 = fabs(r1261966);
        double r1261968 = 1.0213139804930134e+68;
        bool r1261969 = r1261956 <= r1261968;
        double r1261970 = r1261959 / r1261961;
        double r1261971 = r1261963 * r1261956;
        double r1261972 = r1261956 - r1261971;
        double r1261973 = r1261972 / r1261961;
        double r1261974 = r1261970 + r1261973;
        double r1261975 = fabs(r1261974);
        double r1261976 = r1261969 ? r1261975 : r1261967;
        double r1261977 = r1261958 ? r1261967 : r1261976;
        return r1261977;
}

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 < -6.885444965291613e+46 or 1.0213139804930134e+68 < x

    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*0.1

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

    5. Simplified0.1

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

    if -6.885444965291613e+46 < x < 1.0213139804930134e+68

    1. Initial program 2.4

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

    2. Taylor expanded around 0 0.3

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

    3. Simplified2.4

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

    5. Applied associate-*r/0.3

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

    6. Applied sub-div0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.885444965291613 \cdot 10^{+46}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 1.0213139804930134 \cdot 10^{+68}:\\ \;\;\;\;\left|\frac{4}{y} + \frac{x - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019146 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))