Average Error: 1.5 → 0.1
Time: 18.6s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -9.542881099659083 \cdot 10^{+25}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 0.0008878148310546238:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -9.542881099659083 \cdot 10^{+25}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{elif}\;x \le 0.0008878148310546238:\\
\;\;\;\;\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 r946127 = x;
        double r946128 = 4.0;
        double r946129 = r946127 + r946128;
        double r946130 = y;
        double r946131 = r946129 / r946130;
        double r946132 = r946127 / r946130;
        double r946133 = z;
        double r946134 = r946132 * r946133;
        double r946135 = r946131 - r946134;
        double r946136 = fabs(r946135);
        return r946136;
}
↓
double f(double x, double y, double z) {
        double r946137 = x;
        double r946138 = -9.542881099659083e+25;
        bool r946139 = r946137 <= r946138;
        double r946140 = 4.0;
        double r946141 = r946140 + r946137;
        double r946142 = y;
        double r946143 = r946141 / r946142;
        double r946144 = z;
        double r946145 = r946144 / r946142;
        double r946146 = r946137 * r946145;
        double r946147 = r946143 - r946146;
        double r946148 = fabs(r946147);
        double r946149 = 0.0008878148310546238;
        bool r946150 = r946137 <= r946149;
        double r946151 = r946144 * r946137;
        double r946152 = r946141 - r946151;
        double r946153 = r946152 / r946142;
        double r946154 = fabs(r946153);
        double r946155 = r946150 ? r946154 : r946148;
        double r946156 = r946139 ? r946148 : r946155;
        return r946156;
}

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 < -9.542881099659083e+25 or 0.0008878148310546238 < 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*0.2

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

    5. Simplified0.1

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

    if -9.542881099659083e+25 < x < 0.0008878148310546238

    1. Initial program 2.3

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

    3. Applied associate-*l/0.1

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

    4. 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 simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -9.542881099659083 \cdot 10^{+25}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 0.0008878148310546238:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019143 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))