Average Error: 14.1 → 2.4
Time: 1.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.00847826157384981 \cdot 10^{150} \lor \neg \left(\frac{y}{z} \le -9.59916746614835709 \cdot 10^{-156} \lor \neg \left(\frac{y}{z} \le 1.38338 \cdot 10^{-322}\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -3.00847826157384981 \cdot 10^{150} \lor \neg \left(\frac{y}{z} \le -9.59916746614835709 \cdot 10^{-156} \lor \neg \left(\frac{y}{z} \le 1.38338 \cdot 10^{-322}\right)\right):\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r75636 = x;
        double r75637 = y;
        double r75638 = z;
        double r75639 = r75637 / r75638;
        double r75640 = t;
        double r75641 = r75639 * r75640;
        double r75642 = r75641 / r75640;
        double r75643 = r75636 * r75642;
        return r75643;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r75644 = y;
        double r75645 = z;
        double r75646 = r75644 / r75645;
        double r75647 = -3.0084782615738498e+150;
        bool r75648 = r75646 <= r75647;
        double r75649 = -9.599167466148357e-156;
        bool r75650 = r75646 <= r75649;
        double r75651 = 1.3833838083555e-322;
        bool r75652 = r75646 <= r75651;
        double r75653 = !r75652;
        bool r75654 = r75650 || r75653;
        double r75655 = !r75654;
        bool r75656 = r75648 || r75655;
        double r75657 = x;
        double r75658 = r75657 * r75644;
        double r75659 = r75658 / r75645;
        double r75660 = r75645 / r75644;
        double r75661 = r75657 / r75660;
        double r75662 = r75656 ? r75659 : r75661;
        return r75662;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (/ y z) < -3.0084782615738498e+150 or -9.599167466148357e-156 < (/ y z) < 1.3833838083555e-322

    1. Initial program 21.1

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified13.0

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm

    4. Applied associate-*r/1.3

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]

    if -3.0084782615738498e+150 < (/ y z) < -9.599167466148357e-156 or 1.3833838083555e-322 < (/ y z)

    1. Initial program 10.8

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified2.9

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm

    4. Applied associate-*r/8.5

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
    5. Using strategy rm

    6. Applied associate-/l*2.9

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.00847826157384981 \cdot 10^{150} \lor \neg \left(\frac{y}{z} \le -9.59916746614835709 \cdot 10^{-156} \lor \neg \left(\frac{y}{z} \le 1.38338 \cdot 10^{-322}\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))