Average Error: 14.8 → 2.4
Time: 21.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.636613989781371082537060282645406790623 \cdot 10^{235}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -4.268869399178432590236189660705002059275 \cdot 10^{-310}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{y} \cdot \frac{\frac{x}{\sqrt[3]{z}}}{\sqrt[3]{z}}\right) \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -3.636613989781371082537060282645406790623 \cdot 10^{235}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -4.268869399178432590236189660705002059275 \cdot 10^{-310}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r3748683 = x;
        double r3748684 = y;
        double r3748685 = z;
        double r3748686 = r3748684 / r3748685;
        double r3748687 = t;
        double r3748688 = r3748686 * r3748687;
        double r3748689 = r3748688 / r3748687;
        double r3748690 = r3748683 * r3748689;
        return r3748690;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3748691 = y;
        double r3748692 = z;
        double r3748693 = r3748691 / r3748692;
        double r3748694 = -3.636613989781371e+235;
        bool r3748695 = r3748693 <= r3748694;
        double r3748696 = x;
        double r3748697 = r3748696 * r3748691;
        double r3748698 = r3748697 / r3748692;
        double r3748699 = -4.26886939917843e-310;
        bool r3748700 = r3748693 <= r3748699;
        double r3748701 = r3748693 * r3748696;
        double r3748702 = cbrt(r3748691);
        double r3748703 = cbrt(r3748692);
        double r3748704 = r3748696 / r3748703;
        double r3748705 = r3748704 / r3748703;
        double r3748706 = r3748702 * r3748705;
        double r3748707 = r3748706 * r3748702;
        double r3748708 = r3748702 / r3748703;
        double r3748709 = r3748707 * r3748708;
        double r3748710 = r3748700 ? r3748701 : r3748709;
        double r3748711 = r3748695 ? r3748698 : r3748710;
        return r3748711;
}

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) < -3.636613989781371e+235

    1. Initial program 48.0

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

    2. Simplified0.4

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

    if -3.636613989781371e+235 < (/ y z) < -4.26886939917843e-310

    1. Initial program 9.6

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

    2. Simplified8.0

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

    4. Applied *-un-lft-identity8.0

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

    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 -4.26886939917843e-310 < (/ y z)

    1. Initial program 15.5

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

    2. Simplified5.5

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

    4. Applied add-cube-cbrt6.2

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

    5. Applied times-frac5.2

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

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

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

    8. Applied cbrt-prod5.2

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

    9. Applied add-cube-cbrt5.4

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

    10. Applied times-frac5.4

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

    11. Applied associate-*r*4.0

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

    12. Simplified4.0

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.636613989781371082537060282645406790623 \cdot 10^{235}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -4.268869399178432590236189660705002059275 \cdot 10^{-310}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{y} \cdot \frac{\frac{x}{\sqrt[3]{z}}}{\sqrt[3]{z}}\right) \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 +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)))