Average Error: 14.4 → 1.8
Time: 56.2s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.428157915342263 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.4785666758089 \cdot 10^{-318}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.2859174439513116 \cdot 10^{+204}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.428157915342263 \cdot 10^{-204}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 8.4785666758089 \cdot 10^{-318}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 2.2859174439513116 \cdot 10^{+204}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r35249454 = x;
        double r35249455 = y;
        double r35249456 = z;
        double r35249457 = r35249455 / r35249456;
        double r35249458 = t;
        double r35249459 = r35249457 * r35249458;
        double r35249460 = r35249459 / r35249458;
        double r35249461 = r35249454 * r35249460;
        return r35249461;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r35249462 = y;
        double r35249463 = z;
        double r35249464 = r35249462 / r35249463;
        double r35249465 = -5.428157915342263e-204;
        bool r35249466 = r35249464 <= r35249465;
        double r35249467 = x;
        double r35249468 = r35249463 / r35249462;
        double r35249469 = r35249467 / r35249468;
        double r35249470 = 8.4785666758089e-318;
        bool r35249471 = r35249464 <= r35249470;
        double r35249472 = r35249467 * r35249462;
        double r35249473 = r35249472 / r35249463;
        double r35249474 = 2.2859174439513116e+204;
        bool r35249475 = r35249464 <= r35249474;
        double r35249476 = r35249464 * r35249467;
        double r35249477 = r35249475 ? r35249476 : r35249473;
        double r35249478 = r35249471 ? r35249473 : r35249477;
        double r35249479 = r35249466 ? r35249469 : r35249478;
        return r35249479;
}

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 (/ y z) < -5.428157915342263e-204

    1. Initial program 13.2

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

    2. Simplified8.5

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

    4. Applied associate-/l*4.2

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

    if -5.428157915342263e-204 < (/ y z) < 8.4785666758089e-318 or 2.2859174439513116e+204 < (/ y z)

    1. Initial program 22.8

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

    2. Simplified0.5

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

    if 8.4785666758089e-318 < (/ y z) < 2.2859174439513116e+204

    1. Initial program 9.7

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

    2. Simplified8.1

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

    4. Applied add-cube-cbrt8.9

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

    5. Applied times-frac4.9

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

    7. Applied div-inv4.9

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

    8. Applied associate-*l*1.3

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

    9. Simplified0.3

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.428157915342263 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.4785666758089 \cdot 10^{-318}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.2859174439513116 \cdot 10^{+204}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019128 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))