Average Error: 14.2 → 2.0
Time: 12.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 1.4005708519536854 \cdot 10^{-298}:\\ \;\;\;\;\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z}} \cdot \left(\frac{x}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)\\ \mathbf{elif}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 5.155399044473928 \cdot 10^{+268}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 1.4005708519536854 \cdot 10^{-298}:\\
\;\;\;\;\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z}} \cdot \left(\frac{x}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)\\

\mathbf{elif}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 5.155399044473928 \cdot 10^{+268}:\\
\;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r1702737 = x;
        double r1702738 = y;
        double r1702739 = z;
        double r1702740 = r1702738 / r1702739;
        double r1702741 = t;
        double r1702742 = r1702740 * r1702741;
        double r1702743 = r1702742 / r1702741;
        double r1702744 = r1702737 * r1702743;
        return r1702744;
}
↓
double f(double x, double y, double z, double t) {
        double r1702745 = x;
        double r1702746 = y;
        double r1702747 = z;
        double r1702748 = r1702746 / r1702747;
        double r1702749 = t;
        double r1702750 = r1702748 * r1702749;
        double r1702751 = r1702750 / r1702749;
        double r1702752 = r1702745 * r1702751;
        double r1702753 = 1.4005708519536854e-298;
        bool r1702754 = r1702752 <= r1702753;
        double r1702755 = cbrt(r1702746);
        double r1702756 = r1702755 * r1702755;
        double r1702757 = cbrt(r1702747);
        double r1702758 = r1702756 / r1702757;
        double r1702759 = r1702745 / r1702757;
        double r1702760 = r1702755 / r1702757;
        double r1702761 = r1702759 * r1702760;
        double r1702762 = r1702758 * r1702761;
        double r1702763 = 5.155399044473928e+268;
        bool r1702764 = r1702752 <= r1702763;
        double r1702765 = r1702745 * r1702746;
        double r1702766 = r1702765 / r1702747;
        double r1702767 = r1702764 ? r1702752 : r1702766;
        double r1702768 = r1702754 ? r1702762 : r1702767;
        return r1702768;
}

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 (* x (/ (* (/ y z) t) t)) < 1.4005708519536854e-298

    1. Initial program 16.0

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

    2. Simplified4.8

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

    4. Applied add-cube-cbrt5.5

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

    5. Applied *-un-lft-identity5.5

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

    6. Applied times-frac5.5

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

    7. Applied associate-*r*5.0

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

    8. Simplified5.0

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

    10. Applied add-cube-cbrt5.2

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

    11. Applied times-frac5.2

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

    12. Applied associate-*l*2.2

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

    if 1.4005708519536854e-298 < (* x (/ (* (/ y z) t) t)) < 5.155399044473928e+268

    1. Initial program 0.9

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

    if 5.155399044473928e+268 < (* x (/ (* (/ y z) t) t))

    1. Initial program 49.2

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

    2. Simplified6.1

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

    4. Applied associate-*r/5.6

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 1.4005708519536854 \cdot 10^{-298}:\\ \;\;\;\;\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z}} \cdot \left(\frac{x}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)\\ \mathbf{elif}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \le 5.155399044473928 \cdot 10^{+268}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019154 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))