Average Error: 1.7 → 0.7
Time: 50.3s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.572611148022768 \cdot 10^{-182}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 8.927747126101457 \cdot 10^{+27}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \left(z \cdot x\right) \cdot \frac{1}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.572611148022768 \cdot 10^{-182}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{elif}\;x \le 8.927747126101457 \cdot 10^{+27}:\\
\;\;\;\;\left|\frac{4 + x}{y} - \left(z \cdot x\right) \cdot \frac{1}{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 r2719957 = x;
        double r2719958 = 4.0;
        double r2719959 = r2719957 + r2719958;
        double r2719960 = y;
        double r2719961 = r2719959 / r2719960;
        double r2719962 = r2719957 / r2719960;
        double r2719963 = z;
        double r2719964 = r2719962 * r2719963;
        double r2719965 = r2719961 - r2719964;
        double r2719966 = fabs(r2719965);
        return r2719966;
}
↓
double f(double x, double y, double z) {
        double r2719967 = x;
        double r2719968 = -3.572611148022768e-182;
        bool r2719969 = r2719967 <= r2719968;
        double r2719970 = 4.0;
        double r2719971 = r2719970 + r2719967;
        double r2719972 = y;
        double r2719973 = r2719971 / r2719972;
        double r2719974 = z;
        double r2719975 = r2719974 / r2719972;
        double r2719976 = r2719967 * r2719975;
        double r2719977 = r2719973 - r2719976;
        double r2719978 = fabs(r2719977);
        double r2719979 = 8.927747126101457e+27;
        bool r2719980 = r2719967 <= r2719979;
        double r2719981 = r2719974 * r2719967;
        double r2719982 = 1.0;
        double r2719983 = r2719982 / r2719972;
        double r2719984 = r2719981 * r2719983;
        double r2719985 = r2719973 - r2719984;
        double r2719986 = fabs(r2719985);
        double r2719987 = r2719980 ? r2719986 : r2719978;
        double r2719988 = r2719969 ? r2719978 : r2719987;
        return r2719988;
}

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 < -3.572611148022768e-182 or 8.927747126101457e+27 < x

    1. Initial program 1.0

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

    3. Applied div-inv1.0

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

    4. Applied associate-*l*1.3

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

    5. Simplified1.3

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

    if -3.572611148022768e-182 < x < 8.927747126101457e+27

    1. Initial program 2.6

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

    3. Applied div-inv2.6

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

    4. Applied associate-*l*5.7

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

    5. Simplified5.7

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

    7. Applied div-inv5.7

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

    8. Applied associate-*r*0.1

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(x \cdot z\right) \cdot \frac{1}{y}}\right|\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.572611148022768 \cdot 10^{-182}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 8.927747126101457 \cdot 10^{+27}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \left(z \cdot x\right) \cdot \frac{1}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019128 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))