Average Error: 14.1 → 6.1
Time: 14.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.74083005502277 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \le 3.761519737827246 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \le 4.956742987442585 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.74083005502277 \cdot 10^{-271}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;z \le 3.761519737827246 \cdot 10^{-224}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;z \le 4.956742987442585 \cdot 10^{+22}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r3999615 = x;
        double r3999616 = y;
        double r3999617 = z;
        double r3999618 = r3999616 / r3999617;
        double r3999619 = t;
        double r3999620 = r3999618 * r3999619;
        double r3999621 = r3999620 / r3999619;
        double r3999622 = r3999615 * r3999621;
        return r3999622;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3999623 = z;
        double r3999624 = -3.74083005502277e-271;
        bool r3999625 = r3999623 <= r3999624;
        double r3999626 = x;
        double r3999627 = y;
        double r3999628 = r3999623 / r3999627;
        double r3999629 = r3999626 / r3999628;
        double r3999630 = 3.761519737827246e-224;
        bool r3999631 = r3999623 <= r3999630;
        double r3999632 = r3999626 / r3999623;
        double r3999633 = r3999627 * r3999632;
        double r3999634 = 4.956742987442585e+22;
        bool r3999635 = r3999623 <= r3999634;
        double r3999636 = r3999626 * r3999627;
        double r3999637 = r3999636 / r3999623;
        double r3999638 = r3999635 ? r3999629 : r3999637;
        double r3999639 = r3999631 ? r3999633 : r3999638;
        double r3999640 = r3999625 ? r3999629 : r3999639;
        return r3999640;
}

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 3 regimes

  2. if z < -3.74083005502277e-271 or 3.761519737827246e-224 < z < 4.956742987442585e+22

    1. Initial program 13.6

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

    2. Simplified5.6

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

    4. Applied add-cube-cbrt6.5

      \[\leadsto y \cdot \frac{x}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    5. Applied *-un-lft-identity6.5

      \[\leadsto y \cdot \frac{\color{blue}{1 \cdot x}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}\]

    6. Applied times-frac6.5

      \[\leadsto y \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{z}}\right)}\]

    7. Applied associate-*r*5.3

      \[\leadsto \color{blue}{\left(y \cdot \frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{x}{\sqrt[3]{z}}}\]

    8. Simplified5.3

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

    10. Applied *-un-lft-identity5.3

      \[\leadsto \color{blue}{\left(1 \cdot \frac{y}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)} \cdot \frac{x}{\sqrt[3]{z}}\]

    11. Applied associate-*l*5.3

      \[\leadsto \color{blue}{1 \cdot \left(\frac{y}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{z}}\right)}\]

    12. Simplified5.3

      \[\leadsto 1 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]

    if -3.74083005502277e-271 < z < 3.761519737827246e-224

    1. Initial program 21.6

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

    2. Simplified14.2

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

    if 4.956742987442585e+22 < z

    1. Initial program 13.4

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

    2. Simplified5.5

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

    4. Applied associate-*r/6.2

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

  4. Final simplification6.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.74083005502277 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \le 3.761519737827246 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \le 4.956742987442585 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))