Average Error: 14.0 → 2.3
Time: 3.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.45613981804384912 \cdot 10^{278}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -5.31650938160314506 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.3409790596422747 \cdot 10^{-221}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 7.8490367773301062 \cdot 10^{81}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.45613981804384912 \cdot 10^{278}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -5.31650938160314506 \cdot 10^{-21}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 3.3409790596422747 \cdot 10^{-221}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 7.8490367773301062 \cdot 10^{81}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r201985 = x;
        double r201986 = y;
        double r201987 = z;
        double r201988 = r201986 / r201987;
        double r201989 = t;
        double r201990 = r201988 * r201989;
        double r201991 = r201990 / r201989;
        double r201992 = r201985 * r201991;
        return r201992;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r201993 = y;
        double r201994 = z;
        double r201995 = r201993 / r201994;
        double r201996 = -1.456139818043849e+278;
        bool r201997 = r201995 <= r201996;
        double r201998 = x;
        double r201999 = r201998 * r201993;
        double r202000 = r201999 / r201994;
        double r202001 = -5.316509381603145e-21;
        bool r202002 = r201995 <= r202001;
        double r202003 = r201998 * r201995;
        double r202004 = 3.3409790596422747e-221;
        bool r202005 = r201995 <= r202004;
        double r202006 = 7.849036777330106e+81;
        bool r202007 = r201995 <= r202006;
        double r202008 = r201994 / r201993;
        double r202009 = r201998 / r202008;
        double r202010 = r202007 ? r202009 : r202000;
        double r202011 = r202005 ? r202000 : r202010;
        double r202012 = r202002 ? r202003 : r202011;
        double r202013 = r201997 ? r202000 : r202012;
        return r202013;
}

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) < -1.456139818043849e+278 or -5.316509381603145e-21 < (/ y z) < 3.3409790596422747e-221 or 7.849036777330106e+81 < (/ y z)

    1. Initial program 18.6

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

    2. Simplified10.7

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

    4. Applied *-un-lft-identity10.7

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

    5. Applied add-cube-cbrt11.3

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

    6. Applied times-frac11.3

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

    7. Applied associate-*r*4.8

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

    8. Simplified4.8

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

    10. Applied add-cube-cbrt4.9

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

    11. Applied cbrt-prod5.0

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

    12. Taylor expanded around 0 3.9

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

    if -1.456139818043849e+278 < (/ y z) < -5.316509381603145e-21

    1. Initial program 10.4

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

    2. Simplified0.3

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

    if 3.3409790596422747e-221 < (/ y z) < 7.849036777330106e+81

    1. Initial program 6.3

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

    2. Simplified0.2

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

    4. Applied *-un-lft-identity0.2

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

    5. Applied add-cube-cbrt1.3

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

    6. Applied times-frac1.3

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

    7. Applied associate-*r*6.8

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

    8. Simplified6.8

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

    10. Applied add-cube-cbrt6.9

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

    11. Applied cbrt-prod7.0

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

    12. Taylor expanded around 0 10.7

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

    14. Applied associate-/l*0.2

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.45613981804384912 \cdot 10^{278}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -5.31650938160314506 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.3409790596422747 \cdot 10^{-221}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 7.8490367773301062 \cdot 10^{81}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020020 +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)))