Average Error: 13.8 → 5.9
Time: 22.5s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.399464687274639 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \le 3.0447027671553217 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.399464687274639 \cdot 10^{+92}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;y \le 3.0447027671553217 \cdot 10^{-120}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r31112448 = x;
        double r31112449 = y;
        double r31112450 = z;
        double r31112451 = r31112449 / r31112450;
        double r31112452 = t;
        double r31112453 = r31112451 * r31112452;
        double r31112454 = r31112453 / r31112452;
        double r31112455 = r31112448 * r31112454;
        return r31112455;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r31112456 = y;
        double r31112457 = -2.399464687274639e+92;
        bool r31112458 = r31112456 <= r31112457;
        double r31112459 = x;
        double r31112460 = z;
        double r31112461 = r31112460 / r31112456;
        double r31112462 = r31112459 / r31112461;
        double r31112463 = 3.0447027671553217e-120;
        bool r31112464 = r31112456 <= r31112463;
        double r31112465 = r31112460 / r31112459;
        double r31112466 = r31112456 / r31112465;
        double r31112467 = r31112459 * r31112456;
        double r31112468 = r31112467 / r31112460;
        double r31112469 = r31112464 ? r31112466 : r31112468;
        double r31112470 = r31112458 ? r31112462 : r31112469;
        return r31112470;
}

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 < -2.399464687274639e+92

    1. Initial program 19.2

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

    2. Simplified9.9

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

    4. Applied *-un-lft-identity9.9

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

    5. Applied add-cube-cbrt10.8

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

    6. Applied times-frac10.8

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

    7. Applied associate-*r*7.7

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

    8. Taylor expanded around inf 8.8

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

    10. Applied associate-/l*9.5

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

    if -2.399464687274639e+92 < y < 3.0447027671553217e-120

    1. Initial program 12.1

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

    2. Simplified5.2

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

    4. Applied *-un-lft-identity5.2

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

    5. Applied add-cube-cbrt6.0

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

    6. Applied times-frac6.0

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

    7. Applied associate-*r*5.2

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

    9. Applied associate-*r/5.2

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

    10. Applied associate-*l/5.2

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

    11. Simplified5.0

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

    if 3.0447027671553217e-120 < y

    1. Initial program 14.4

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

    2. Simplified5.1

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

    4. Applied *-un-lft-identity5.1

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

    5. Applied add-cube-cbrt6.0

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

    6. Applied times-frac6.0

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

    7. Applied associate-*r*5.5

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

    8. Taylor expanded around inf 5.8

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

  4. Final simplification5.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.399464687274639 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \le 3.0447027671553217 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019120 +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)))