Average Error: 1.7 → 0.3
Time: 3.9s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.09954904008270574 \cdot 10^{-121}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 4360323.74267882574:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.09954904008270574 \cdot 10^{-121}:\\
\;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{elif}\;x \le 4360323.74267882574:\\
\;\;\;\;\left|\frac{x + 4}{y} - \frac{x \cdot z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r56819 = x;
        double r56820 = 4.0;
        double r56821 = r56819 + r56820;
        double r56822 = y;
        double r56823 = r56821 / r56822;
        double r56824 = r56819 / r56822;
        double r56825 = z;
        double r56826 = r56824 * r56825;
        double r56827 = r56823 - r56826;
        double r56828 = fabs(r56827);
        return r56828;
}
↓
double f(double x, double y, double z) {
        double r56829 = x;
        double r56830 = -1.0995490400827057e-121;
        bool r56831 = r56829 <= r56830;
        double r56832 = 4.0;
        double r56833 = r56829 + r56832;
        double r56834 = y;
        double r56835 = r56833 / r56834;
        double r56836 = z;
        double r56837 = r56836 / r56834;
        double r56838 = r56829 * r56837;
        double r56839 = r56835 - r56838;
        double r56840 = fabs(r56839);
        double r56841 = 4360323.742678826;
        bool r56842 = r56829 <= r56841;
        double r56843 = r56829 * r56836;
        double r56844 = r56843 / r56834;
        double r56845 = r56835 - r56844;
        double r56846 = fabs(r56845);
        double r56847 = r56829 / r56834;
        double r56848 = r56847 * r56836;
        double r56849 = r56835 - r56848;
        double r56850 = fabs(r56849);
        double r56851 = r56842 ? r56846 : r56850;
        double r56852 = r56831 ? r56840 : r56851;
        return r56852;
}

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 3 regimes

  2. if x < -1.0995490400827057e-121

    1. Initial program 0.9

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

    3. Applied div-inv0.9

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

    4. Applied associate-*l*1.0

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

    5. Simplified0.9

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

    if -1.0995490400827057e-121 < x < 4360323.742678826

    1. Initial program 2.8

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

    3. Applied div-inv2.8

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

    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 associate-*r/0.1

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

    if 4360323.742678826 < x

    1. Initial program 0.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.09954904008270574 \cdot 10^{-121}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 4360323.74267882574:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))