Average Error: 1.7 → 1.2
Time: 9.8s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.775517148444541890019330037710355464013 \cdot 10^{50} \lor \neg \left(x \le 2.295099393231360663003372969170030877664 \cdot 10^{-243}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.775517148444541890019330037710355464013 \cdot 10^{50} \lor \neg \left(x \le 2.295099393231360663003372969170030877664 \cdot 10^{-243}\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 r17457 = x;
        double r17458 = 4.0;
        double r17459 = r17457 + r17458;
        double r17460 = y;
        double r17461 = r17459 / r17460;
        double r17462 = r17457 / r17460;
        double r17463 = z;
        double r17464 = r17462 * r17463;
        double r17465 = r17461 - r17464;
        double r17466 = fabs(r17465);
        return r17466;
}
↓
double f(double x, double y, double z) {
        double r17467 = x;
        double r17468 = -2.775517148444542e+50;
        bool r17469 = r17467 <= r17468;
        double r17470 = 2.2950993932313607e-243;
        bool r17471 = r17467 <= r17470;
        double r17472 = !r17471;
        bool r17473 = r17469 || r17472;
        double r17474 = 4.0;
        double r17475 = r17467 + r17474;
        double r17476 = y;
        double r17477 = r17475 / r17476;
        double r17478 = z;
        double r17479 = r17478 / r17476;
        double r17480 = r17467 * r17479;
        double r17481 = r17477 - r17480;
        double r17482 = fabs(r17481);
        double r17483 = r17467 * r17478;
        double r17484 = r17475 - r17483;
        double r17485 = r17484 / r17476;
        double r17486 = fabs(r17485);
        double r17487 = r17473 ? r17482 : r17486;
        return r17487;
}

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 < -2.775517148444542e+50 or 2.2950993932313607e-243 < x

    1. Initial program 1.2

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

    3. Applied div-inv1.2

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

    4. Applied associate-*l*2.0

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

    5. Simplified2.0

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

    if -2.775517148444542e+50 < x < 2.2950993932313607e-243

    1. Initial program 2.4

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

    3. Applied associate-*l/0.3

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

    4. Applied sub-div0.3

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.775517148444541890019330037710355464013 \cdot 10^{50} \lor \neg \left(x \le 2.295099393231360663003372969170030877664 \cdot 10^{-243}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))