Average Error: 14.4 → 2.7
Time: 16.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.428157915342263 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.763171201931148 \cdot 10^{-300}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{z}}} \cdot \left(\frac{x}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{y}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right)\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -5.428157915342263 \cdot 10^{-204}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 1.763171201931148 \cdot 10^{-300}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{z}}} \cdot \left(\frac{x}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{y}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r1877597 = x;
        double r1877598 = y;
        double r1877599 = z;
        double r1877600 = r1877598 / r1877599;
        double r1877601 = t;
        double r1877602 = r1877600 * r1877601;
        double r1877603 = r1877602 / r1877601;
        double r1877604 = r1877597 * r1877603;
        return r1877604;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r1877605 = y;
        double r1877606 = z;
        double r1877607 = r1877605 / r1877606;
        double r1877608 = -5.428157915342263e-204;
        bool r1877609 = r1877607 <= r1877608;
        double r1877610 = x;
        double r1877611 = r1877606 / r1877605;
        double r1877612 = r1877610 / r1877611;
        double r1877613 = 1.763171201931148e-300;
        bool r1877614 = r1877607 <= r1877613;
        double r1877615 = r1877610 * r1877605;
        double r1877616 = r1877615 / r1877606;
        double r1877617 = cbrt(r1877605);
        double r1877618 = cbrt(r1877606);
        double r1877619 = cbrt(r1877618);
        double r1877620 = r1877617 / r1877619;
        double r1877621 = r1877618 * r1877618;
        double r1877622 = r1877621 / r1877617;
        double r1877623 = r1877610 / r1877622;
        double r1877624 = cbrt(r1877621);
        double r1877625 = r1877617 / r1877624;
        double r1877626 = r1877623 * r1877625;
        double r1877627 = r1877620 * r1877626;
        double r1877628 = r1877614 ? r1877616 : r1877627;
        double r1877629 = r1877609 ? r1877612 : r1877628;
        return r1877629;
}

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) < -5.428157915342263e-204

    1. Initial program 13.2

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

    2. Simplified8.5

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

    4. Applied associate-/l*4.2

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

    if -5.428157915342263e-204 < (/ y z) < 1.763171201931148e-300

    1. Initial program 17.5

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

    2. Simplified0.3

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

    if 1.763171201931148e-300 < (/ y z)

    1. Initial program 13.8

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

    2. Simplified7.4

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

    4. Applied add-cube-cbrt8.3

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

    5. Applied times-frac5.4

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

    7. Applied add-cube-cbrt5.4

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

    8. Applied cbrt-prod5.5

      \[\leadsto \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\color{blue}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}\]

    9. Applied add-cube-cbrt5.7

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

    10. Applied times-frac5.7

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

    11. Applied associate-*r*4.9

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

    13. Applied *-un-lft-identity4.9

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

    14. Applied times-frac4.9

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

    15. Applied associate-*r*4.9

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

    16. Simplified2.5

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

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.428157915342263 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.763171201931148 \cdot 10^{-300}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{z}}} \cdot \left(\frac{x}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{y}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019128 +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)))