Average Error: 14.2 → 0.3
Time: 45.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.2521697391721805 \cdot 10^{+183}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -3.917190651235875 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.2214116120111555 \cdot 10^{-224}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 3.067025007758323 \cdot 10^{+241}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.2521697391721805 \cdot 10^{+183}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -3.917190651235875 \cdot 10^{-264}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 1.2214116120111555 \cdot 10^{-224}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\mathbf{elif}\;\frac{y}{z} \le 3.067025007758323 \cdot 10^{+241}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r15828753 = x;
        double r15828754 = y;
        double r15828755 = z;
        double r15828756 = r15828754 / r15828755;
        double r15828757 = t;
        double r15828758 = r15828756 * r15828757;
        double r15828759 = r15828758 / r15828757;
        double r15828760 = r15828753 * r15828759;
        return r15828760;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r15828761 = y;
        double r15828762 = z;
        double r15828763 = r15828761 / r15828762;
        double r15828764 = -2.2521697391721805e+183;
        bool r15828765 = r15828763 <= r15828764;
        double r15828766 = x;
        double r15828767 = r15828766 * r15828761;
        double r15828768 = r15828767 / r15828762;
        double r15828769 = -3.917190651235875e-264;
        bool r15828770 = r15828763 <= r15828769;
        double r15828771 = r15828763 * r15828766;
        double r15828772 = 1.2214116120111555e-224;
        bool r15828773 = r15828763 <= r15828772;
        double r15828774 = r15828762 / r15828766;
        double r15828775 = r15828761 / r15828774;
        double r15828776 = 3.067025007758323e+241;
        bool r15828777 = r15828763 <= r15828776;
        double r15828778 = r15828777 ? r15828771 : r15828768;
        double r15828779 = r15828773 ? r15828775 : r15828778;
        double r15828780 = r15828770 ? r15828771 : r15828779;
        double r15828781 = r15828765 ? r15828768 : r15828780;
        return r15828781;
}

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) < -2.2521697391721805e+183 or 3.067025007758323e+241 < (/ y z)

    1. Initial program 40.4

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

    2. Simplified28.2

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

    4. Applied *-un-lft-identity28.2

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

    5. Applied add-cube-cbrt28.8

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

    6. Applied times-frac28.8

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

    7. Applied associate-*r*7.8

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

    8. Taylor expanded around 0 1.0

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

    if -2.2521697391721805e+183 < (/ y z) < -3.917190651235875e-264 or 1.2214116120111555e-224 < (/ y z) < 3.067025007758323e+241

    1. Initial program 8.3

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

    2. Simplified0.2

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

    if -3.917190651235875e-264 < (/ y z) < 1.2214116120111555e-224

    1. Initial program 17.8

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

    2. Simplified12.9

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

    4. Applied *-un-lft-identity12.9

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

    5. Applied add-cube-cbrt13.1

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

    6. Applied times-frac13.1

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

    7. Applied associate-*r*2.5

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

    9. Applied associate-*r/2.5

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

    10. Applied associate-*l/2.5

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

    11. Simplified0.2

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{z}{x}}}}{1}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.2521697391721805 \cdot 10^{+183}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -3.917190651235875 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.2214116120111555 \cdot 10^{-224}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 3.067025007758323 \cdot 10^{+241}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019119 +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)))