Average Error: 15.3 → 0.6
Time: 12.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -4.271360513759333161781280648465473250074 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -0.0 \lor \neg \left(\frac{y}{z} \le 9.193416187857939378229423416553993724805 \cdot 10^{231}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} = -\infty:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le -4.271360513759333161781280648465473250074 \cdot 10^{-161}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -0.0 \lor \neg \left(\frac{y}{z} \le 9.193416187857939378229423416553993724805 \cdot 10^{231}\right):\\
\;\;\;\;\frac{y \cdot x}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r81838 = x;
        double r81839 = y;
        double r81840 = z;
        double r81841 = r81839 / r81840;
        double r81842 = t;
        double r81843 = r81841 * r81842;
        double r81844 = r81843 / r81842;
        double r81845 = r81838 * r81844;
        return r81845;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r81846 = y;
        double r81847 = z;
        double r81848 = r81846 / r81847;
        double r81849 = -inf.0;
        bool r81850 = r81848 <= r81849;
        double r81851 = 1.0;
        double r81852 = x;
        double r81853 = r81847 / r81852;
        double r81854 = r81853 / r81846;
        double r81855 = r81851 / r81854;
        double r81856 = -4.271360513759333e-161;
        bool r81857 = r81848 <= r81856;
        double r81858 = r81852 * r81848;
        double r81859 = -0.0;
        bool r81860 = r81848 <= r81859;
        double r81861 = 9.19341618785794e+231;
        bool r81862 = r81848 <= r81861;
        double r81863 = !r81862;
        bool r81864 = r81860 || r81863;
        double r81865 = r81846 * r81852;
        double r81866 = r81865 / r81847;
        double r81867 = r81847 / r81846;
        double r81868 = r81852 / r81867;
        double r81869 = r81864 ? r81866 : r81868;
        double r81870 = r81857 ? r81858 : r81869;
        double r81871 = r81850 ? r81855 : r81870;
        return r81871;
}

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

    1. Initial program 64.0

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

    2. Simplified0.3

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

    4. Applied clear-num0.4

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

    5. Simplified0.4

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

    if -inf.0 < (/ y z) < -4.271360513759333e-161

    1. Initial program 10.6

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

    2. Simplified9.4

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

    4. Applied *-un-lft-identity9.4

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

    5. Applied times-frac0.3

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

    6. Simplified0.3

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

    if -4.271360513759333e-161 < (/ y z) < -0.0 or 9.19341618785794e+231 < (/ y z)

    1. Initial program 22.3

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

    2. Simplified0.8

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

    if -0.0 < (/ y z) < 9.19341618785794e+231

    1. Initial program 10.8

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

    2. Simplified7.4

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

    4. Applied associate-/l*0.7

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -4.271360513759333161781280648465473250074 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -0.0 \lor \neg \left(\frac{y}{z} \le 9.193416187857939378229423416553993724805 \cdot 10^{231}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))