Average Error: 14.1 → 6.1
Time: 15.7s
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 r5476314 = x;
        double r5476315 = y;
        double r5476316 = z;
        double r5476317 = r5476315 / r5476316;
        double r5476318 = t;
        double r5476319 = r5476317 * r5476318;
        double r5476320 = r5476319 / r5476318;
        double r5476321 = r5476314 * r5476320;
        return r5476321;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r5476322 = z;
        double r5476323 = -3.74083005502277e-271;
        bool r5476324 = r5476322 <= r5476323;
        double r5476325 = x;
        double r5476326 = y;
        double r5476327 = r5476322 / r5476326;
        double r5476328 = r5476325 / r5476327;
        double r5476329 = 3.761519737827246e-224;
        bool r5476330 = r5476322 <= r5476329;
        double r5476331 = r5476325 / r5476322;
        double r5476332 = r5476326 * r5476331;
        double r5476333 = 4.956742987442585e+22;
        bool r5476334 = r5476322 <= r5476333;
        double r5476335 = r5476325 * r5476326;
        double r5476336 = r5476335 / r5476322;
        double r5476337 = r5476334 ? r5476328 : r5476336;
        double r5476338 = r5476330 ? r5476332 : r5476337;
        double r5476339 = r5476324 ? r5476328 : r5476338;
        return r5476339;
}

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)))