Average Error: 15.3 → 0.7
Time: 11.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.548240730790440881436662006949490760264 \cdot 10^{219}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.442433262831919710603838797359517016977 \cdot 10^{-140}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0 \lor \neg \left(\frac{y}{z} \le 2.381732747802579320943017921487277387689 \cdot 10^{244}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.548240730790440881436662006949490760264 \cdot 10^{219}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.442433262831919710603838797359517016977 \cdot 10^{-140}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le -0.0 \lor \neg \left(\frac{y}{z} \le 2.381732747802579320943017921487277387689 \cdot 10^{244}\right):\\
\;\;\;\;y \cdot \frac{x}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r80874 = x;
        double r80875 = y;
        double r80876 = z;
        double r80877 = r80875 / r80876;
        double r80878 = t;
        double r80879 = r80877 * r80878;
        double r80880 = r80879 / r80878;
        double r80881 = r80874 * r80880;
        return r80881;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r80882 = y;
        double r80883 = z;
        double r80884 = r80882 / r80883;
        double r80885 = -1.548240730790441e+219;
        bool r80886 = r80884 <= r80885;
        double r80887 = x;
        double r80888 = r80887 / r80883;
        double r80889 = r80882 * r80888;
        double r80890 = -1.4424332628319197e-140;
        bool r80891 = r80884 <= r80890;
        double r80892 = r80884 * r80887;
        double r80893 = -0.0;
        bool r80894 = r80884 <= r80893;
        double r80895 = 2.3817327478025793e+244;
        bool r80896 = r80884 <= r80895;
        double r80897 = !r80896;
        bool r80898 = r80894 || r80897;
        double r80899 = r80883 / r80882;
        double r80900 = r80887 / r80899;
        double r80901 = r80898 ? r80889 : r80900;
        double r80902 = r80891 ? r80892 : r80901;
        double r80903 = r80886 ? r80889 : r80902;
        return r80903;
}

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) < -1.548240730790441e+219 or -1.4424332628319197e-140 < (/ y z) < -0.0 or 2.3817327478025793e+244 < (/ y z)

    1. Initial program 25.6

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

    2. Simplified1.0

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

    3. Taylor expanded around 0 1.0

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

    4. Simplified0.9

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

    if -1.548240730790441e+219 < (/ y z) < -1.4424332628319197e-140

    1. Initial program 8.5

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

    2. Simplified10.5

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

    4. Applied *-un-lft-identity10.5

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

    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 -0.0 < (/ y z) < 2.3817327478025793e+244

    1. Initial program 10.9

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

    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 3 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.548240730790440881436662006949490760264 \cdot 10^{219}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.442433262831919710603838797359517016977 \cdot 10^{-140}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0 \lor \neg \left(\frac{y}{z} \le 2.381732747802579320943017921487277387689 \cdot 10^{244}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

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