Average Error: 14.8 → 0.3
Time: 2.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.032946575227289082299442188903898755778 \cdot 10^{-265}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.707355746264835359667361500171699768251 \cdot 10^{-300}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 7.166584424187464259231246965323639075754 \cdot 10^{225}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]
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 -2.032946575227289082299442188903898755778 \cdot 10^{-265}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 1.707355746264835359667361500171699768251 \cdot 10^{-300}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\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 r151891 = x;
        double r151892 = y;
        double r151893 = z;
        double r151894 = r151892 / r151893;
        double r151895 = t;
        double r151896 = r151894 * r151895;
        double r151897 = r151896 / r151895;
        double r151898 = r151891 * r151897;
        return r151898;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r151899 = y;
        double r151900 = z;
        double r151901 = r151899 / r151900;
        double r151902 = -inf.0;
        bool r151903 = r151901 <= r151902;
        double r151904 = 1.0;
        double r151905 = x;
        double r151906 = r151905 * r151899;
        double r151907 = r151900 / r151906;
        double r151908 = r151904 / r151907;
        double r151909 = -2.032946575227289e-265;
        bool r151910 = r151901 <= r151909;
        double r151911 = r151900 / r151899;
        double r151912 = r151905 / r151911;
        double r151913 = 1.7073557462648354e-300;
        bool r151914 = r151901 <= r151913;
        double r151915 = 7.166584424187464e+225;
        bool r151916 = r151901 <= r151915;
        double r151917 = r151905 * r151901;
        double r151918 = r151916 ? r151917 : r151908;
        double r151919 = r151914 ? r151908 : r151918;
        double r151920 = r151910 ? r151912 : r151919;
        double r151921 = r151903 ? r151908 : r151920;
        return r151921;
}

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) < -inf.0 or -2.032946575227289e-265 < (/ y z) < 1.7073557462648354e-300 or 7.166584424187464e+225 < (/ y z)

    1. Initial program 29.1

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

    2. Simplified24.1

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

    4. Applied associate-*r/0.3

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

    6. Applied clear-num0.7

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

    if -inf.0 < (/ y z) < -2.032946575227289e-265

    1. Initial program 10.6

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

    2. Simplified0.2

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

    4. Applied associate-*r/8.2

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

    6. Applied associate-/l*0.2

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

    if 1.7073557462648354e-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 3 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.032946575227289082299442188903898755778 \cdot 10^{-265}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.707355746264835359667361500171699768251 \cdot 10^{-300}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 7.166584424187464259231246965323639075754 \cdot 10^{225}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(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)))