Average Error: 1.7 → 0.4
Time: 14.3s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.6359444841938246 \cdot 10^{+35}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 4.712266768697627 \cdot 10^{-112}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.6359444841938246 \cdot 10^{+35}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{elif}\;x \le 4.712266768697627 \cdot 10^{-112}:\\
\;\;\;\;\left|\frac{\left(4 + x\right) - 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 r1012026 = x;
        double r1012027 = 4.0;
        double r1012028 = r1012026 + r1012027;
        double r1012029 = y;
        double r1012030 = r1012028 / r1012029;
        double r1012031 = r1012026 / r1012029;
        double r1012032 = z;
        double r1012033 = r1012031 * r1012032;
        double r1012034 = r1012030 - r1012033;
        double r1012035 = fabs(r1012034);
        return r1012035;
}
↓
double f(double x, double y, double z) {
        double r1012036 = x;
        double r1012037 = -1.6359444841938246e+35;
        bool r1012038 = r1012036 <= r1012037;
        double r1012039 = 4.0;
        double r1012040 = r1012039 + r1012036;
        double r1012041 = y;
        double r1012042 = r1012040 / r1012041;
        double r1012043 = z;
        double r1012044 = r1012043 / r1012041;
        double r1012045 = r1012036 * r1012044;
        double r1012046 = r1012042 - r1012045;
        double r1012047 = fabs(r1012046);
        double r1012048 = 4.712266768697627e-112;
        bool r1012049 = r1012036 <= r1012048;
        double r1012050 = r1012043 * r1012036;
        double r1012051 = r1012040 - r1012050;
        double r1012052 = r1012051 / r1012041;
        double r1012053 = fabs(r1012052);
        double r1012054 = r1012049 ? r1012053 : r1012047;
        double r1012055 = r1012038 ? r1012047 : r1012054;
        return r1012055;
}

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 < -1.6359444841938246e+35 or 4.712266768697627e-112 < x

    1. Initial program 0.7

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

    3. Applied div-inv0.7

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

    4. Applied associate-*l*0.9

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

    5. Simplified0.8

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

    if -1.6359444841938246e+35 < x < 4.712266768697627e-112

    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*5.6

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

    5. Simplified5.6

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

    7. Applied associate-*r/0.1

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

    8. 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 simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.6359444841938246 \cdot 10^{+35}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 4.712266768697627 \cdot 10^{-112}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019139 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))