Average Error: 14.8 → 0.3
Time: 2.5s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.434471595776521596384923059287499479756 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.707355746264835359667361500171699768251 \cdot 10^{-300}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 7.166584424187464259231246965323639075754 \cdot 10^{225}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} = -\infty:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;\frac{y}{z} \le -1.434471595776521596384923059287499479756 \cdot 10^{-254}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 1.707355746264835359667361500171699768251 \cdot 10^{-300}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 7.166584424187464259231246965323639075754 \cdot 10^{225}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r148395 = x;
        double r148396 = y;
        double r148397 = z;
        double r148398 = r148396 / r148397;
        double r148399 = t;
        double r148400 = r148398 * r148399;
        double r148401 = r148400 / r148399;
        double r148402 = r148395 * r148401;
        return r148402;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r148403 = y;
        double r148404 = z;
        double r148405 = r148403 / r148404;
        double r148406 = -inf.0;
        bool r148407 = r148405 <= r148406;
        double r148408 = 1.0;
        double r148409 = x;
        double r148410 = r148409 * r148403;
        double r148411 = r148404 / r148410;
        double r148412 = r148408 / r148411;
        double r148413 = -1.4344715957765216e-254;
        bool r148414 = r148405 <= r148413;
        double r148415 = r148404 / r148403;
        double r148416 = r148409 / r148415;
        double r148417 = 1.7073557462648354e-300;
        bool r148418 = r148405 <= r148417;
        double r148419 = r148410 / r148404;
        double r148420 = 7.166584424187464e+225;
        bool r148421 = r148405 <= r148420;
        double r148422 = r148409 * r148405;
        double r148423 = r148421 ? r148422 : r148412;
        double r148424 = r148418 ? r148419 : r148423;
        double r148425 = r148414 ? r148416 : r148424;
        double r148426 = r148407 ? r148412 : r148425;
        return r148426;
}

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 4 regimes

  2. if (/ y z) < -inf.0 or 7.166584424187464e+225 < (/ y z)

    1. Initial program 53.1

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

    2. Simplified43.1

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

    4. Applied associate-*r/0.8

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

    6. Applied clear-num0.8

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

    if -inf.0 < (/ y z) < -1.4344715957765216e-254

    1. Initial program 10.4

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

    2. Simplified0.2

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

    4. Applied associate-*r/8.3

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

    6. Applied associate-/l*0.2

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

    if -1.4344715957765216e-254 < (/ y z) < 1.7073557462648354e-300

    1. Initial program 19.0

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

    2. Simplified15.3

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

    4. Applied associate-*r/0.1

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

    if 1.7073557462648354e-300 < (/ y z) < 7.166584424187464e+225

    1. Initial program 9.1

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

    2. Simplified0.2

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -1.434471595776521596384923059287499479756 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.707355746264835359667361500171699768251 \cdot 10^{-300}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 7.166584424187464259231246965323639075754 \cdot 10^{225}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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)))