Average Error: 1.6 → 0.1
Time: 1.0m
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.429102782305307 \cdot 10^{+43}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 1.4338863214513387 \cdot 10^{-10}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.429102782305307 \cdot 10^{+43}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{elif}\;x \le 1.4338863214513387 \cdot 10^{-10}:\\
\;\;\;\;\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 r3717212 = x;
        double r3717213 = 4.0;
        double r3717214 = r3717212 + r3717213;
        double r3717215 = y;
        double r3717216 = r3717214 / r3717215;
        double r3717217 = r3717212 / r3717215;
        double r3717218 = z;
        double r3717219 = r3717217 * r3717218;
        double r3717220 = r3717216 - r3717219;
        double r3717221 = fabs(r3717220);
        return r3717221;
}
↓
double f(double x, double y, double z) {
        double r3717222 = x;
        double r3717223 = -4.429102782305307e+43;
        bool r3717224 = r3717222 <= r3717223;
        double r3717225 = 4.0;
        double r3717226 = r3717225 + r3717222;
        double r3717227 = y;
        double r3717228 = r3717226 / r3717227;
        double r3717229 = z;
        double r3717230 = r3717229 / r3717227;
        double r3717231 = r3717222 * r3717230;
        double r3717232 = r3717228 - r3717231;
        double r3717233 = fabs(r3717232);
        double r3717234 = 1.4338863214513387e-10;
        bool r3717235 = r3717222 <= r3717234;
        double r3717236 = r3717229 * r3717222;
        double r3717237 = r3717226 - r3717236;
        double r3717238 = r3717237 / r3717227;
        double r3717239 = fabs(r3717238);
        double r3717240 = r3717235 ? r3717239 : r3717233;
        double r3717241 = r3717224 ? r3717233 : r3717240;
        return r3717241;
}

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 < -4.429102782305307e+43 or 1.4338863214513387e-10 < 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 -4.429102782305307e+43 < x < 1.4338863214513387e-10

    1. Initial program 2.4

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

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.429102782305307 \cdot 10^{+43}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 1.4338863214513387 \cdot 10^{-10}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019125 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))