Average Error: 1.4 → 0.2
Time: 2.8s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -7.609461543067301 \cdot 10^{55} \lor \neg \left(x \le 2083989822.488266\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -7.609461543067301 \cdot 10^{55} \lor \neg \left(x \le 2083989822.488266\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r25259 = x;
        double r25260 = 4.0;
        double r25261 = r25259 + r25260;
        double r25262 = y;
        double r25263 = r25261 / r25262;
        double r25264 = r25259 / r25262;
        double r25265 = z;
        double r25266 = r25264 * r25265;
        double r25267 = r25263 - r25266;
        double r25268 = fabs(r25267);
        return r25268;
}
↓
double f(double x, double y, double z) {
        double r25269 = x;
        double r25270 = -7.609461543067301e+55;
        bool r25271 = r25269 <= r25270;
        double r25272 = 2083989822.488266;
        bool r25273 = r25269 <= r25272;
        double r25274 = !r25273;
        bool r25275 = r25271 || r25274;
        double r25276 = 4.0;
        double r25277 = r25269 + r25276;
        double r25278 = y;
        double r25279 = r25277 / r25278;
        double r25280 = z;
        double r25281 = r25280 / r25278;
        double r25282 = r25269 * r25281;
        double r25283 = r25279 - r25282;
        double r25284 = fabs(r25283);
        double r25285 = r25269 * r25280;
        double r25286 = r25277 - r25285;
        double r25287 = r25286 / r25278;
        double r25288 = fabs(r25287);
        double r25289 = r25275 ? r25284 : r25288;
        return r25289;
}

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 < -7.609461543067301e+55 or 2083989822.488266 < 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 -7.609461543067301e+55 < x < 2083989822.488266

    1. Initial program 2.1

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

    3. Applied associate-*l/0.2

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

    4. Applied sub-div0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -7.609461543067301 \cdot 10^{55} \lor \neg \left(x \le 2083989822.488266\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))