Average Error: 14.2 → 1.8
Time: 31.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -8.915792043631097 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -4.146146087892682 \cdot 10^{-154}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.694613998864896 \cdot 10^{+57}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -8.915792043631097 \cdot 10^{+76}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -4.146146087892682 \cdot 10^{-154}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le -0.0:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 3.694613998864896 \cdot 10^{+57}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r34151915 = x;
        double r34151916 = y;
        double r34151917 = z;
        double r34151918 = r34151916 / r34151917;
        double r34151919 = t;
        double r34151920 = r34151918 * r34151919;
        double r34151921 = r34151920 / r34151919;
        double r34151922 = r34151915 * r34151921;
        return r34151922;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r34151923 = y;
        double r34151924 = z;
        double r34151925 = r34151923 / r34151924;
        double r34151926 = -8.915792043631097e+76;
        bool r34151927 = r34151925 <= r34151926;
        double r34151928 = x;
        double r34151929 = r34151928 / r34151924;
        double r34151930 = r34151923 * r34151929;
        double r34151931 = -4.146146087892682e-154;
        bool r34151932 = r34151925 <= r34151931;
        double r34151933 = r34151925 * r34151928;
        double r34151934 = -0.0;
        bool r34151935 = r34151925 <= r34151934;
        double r34151936 = 3.694613998864896e+57;
        bool r34151937 = r34151925 <= r34151936;
        double r34151938 = r34151937 ? r34151933 : r34151930;
        double r34151939 = r34151935 ? r34151930 : r34151938;
        double r34151940 = r34151932 ? r34151933 : r34151939;
        double r34151941 = r34151927 ? r34151930 : r34151940;
        return r34151941;
}

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 2 regimes

  2. if (/ y z) < -8.915792043631097e+76 or -4.146146087892682e-154 < (/ y z) < -0.0 or 3.694613998864896e+57 < (/ y z)

    1. Initial program 21.1

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

    2. Simplified10.6

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

    4. Applied add-cube-cbrt11.2

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

    5. Applied *-un-lft-identity11.2

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

    6. Applied times-frac11.2

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

    7. Applied associate-*r*4.2

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

    9. Applied add-cbrt-cube4.3

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

    11. Applied pow14.3

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

    12. Applied pow14.3

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

    13. Applied pow-prod-down4.3

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

    14. Simplified3.0

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

    if -8.915792043631097e+76 < (/ y z) < -4.146146087892682e-154 or -0.0 < (/ y z) < 3.694613998864896e+57

    1. Initial program 6.7

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

    2. Simplified0.4

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -8.915792043631097 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -4.146146087892682 \cdot 10^{-154}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.694613998864896 \cdot 10^{+57}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019112 +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)))