Average Error: 14.8 → 0.5
Time: 16.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.422773879432081316361824486038416445882 \cdot 10^{151}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{elif}\;\frac{y}{z} \le -5.10484190542812669037692225063426301177 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.774265247967482801945189091940352026471 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 2.981277762077973021880053045655171198882 \cdot 10^{261}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.422773879432081316361824486038416445882 \cdot 10^{151}:\\
\;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\

\mathbf{elif}\;\frac{y}{z} \le -5.10484190542812669037692225063426301177 \cdot 10^{-201}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 2.774265247967482801945189091940352026471 \cdot 10^{-185}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;\frac{y}{z} \le 2.981277762077973021880053045655171198882 \cdot 10^{261}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r3345854 = x;
        double r3345855 = y;
        double r3345856 = z;
        double r3345857 = r3345855 / r3345856;
        double r3345858 = t;
        double r3345859 = r3345857 * r3345858;
        double r3345860 = r3345859 / r3345858;
        double r3345861 = r3345854 * r3345860;
        return r3345861;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3345862 = y;
        double r3345863 = z;
        double r3345864 = r3345862 / r3345863;
        double r3345865 = -5.422773879432081e+151;
        bool r3345866 = r3345864 <= r3345865;
        double r3345867 = 1.0;
        double r3345868 = x;
        double r3345869 = r3345862 * r3345868;
        double r3345870 = r3345863 / r3345869;
        double r3345871 = r3345867 / r3345870;
        double r3345872 = -5.104841905428127e-201;
        bool r3345873 = r3345864 <= r3345872;
        double r3345874 = r3345868 * r3345864;
        double r3345875 = 2.7742652479674828e-185;
        bool r3345876 = r3345864 <= r3345875;
        double r3345877 = r3345868 / r3345863;
        double r3345878 = r3345877 * r3345862;
        double r3345879 = 2.981277762077973e+261;
        bool r3345880 = r3345864 <= r3345879;
        double r3345881 = r3345880 ? r3345874 : r3345878;
        double r3345882 = r3345876 ? r3345878 : r3345881;
        double r3345883 = r3345873 ? r3345874 : r3345882;
        double r3345884 = r3345866 ? r3345871 : r3345883;
        return r3345884;
}

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) < -5.422773879432081e+151

    1. Initial program 36.5

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

    2. Simplified2.3

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

    4. Applied clear-num2.4

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

    if -5.422773879432081e+151 < (/ y z) < -5.104841905428127e-201 or 2.7742652479674828e-185 < (/ y z) < 2.981277762077973e+261

    1. Initial program 8.2

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

    2. Simplified10.1

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

    4. Applied *-un-lft-identity10.1

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

    5. Applied times-frac0.2

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

    6. Simplified0.2

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

    if -5.104841905428127e-201 < (/ y z) < 2.7742652479674828e-185 or 2.981277762077973e+261 < (/ y z)

    1. Initial program 21.4

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

    2. Simplified0.4

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

    4. Applied div-inv0.4

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

    6. Applied pow10.4

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

    7. Applied pow10.4

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

    8. Applied pow10.4

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

    9. Applied pow-prod-down0.4

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

    10. Applied pow-prod-down0.4

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

    11. Simplified0.6

      \[\leadsto {\color{blue}{\left(\frac{x}{z} \cdot y\right)}}^{1}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.422773879432081316361824486038416445882 \cdot 10^{151}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{elif}\;\frac{y}{z} \le -5.10484190542812669037692225063426301177 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.774265247967482801945189091940352026471 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 2.981277762077973021880053045655171198882 \cdot 10^{261}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 +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)))