Average Error: 15.1 → 1.3
Time: 27.0s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.636236528901048215946534163640858695462 \cdot 10^{270}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.631110063090909634837685639348743915595 \cdot 10^{-306}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot x\right)\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -4.636236528901048215946534163640858695462 \cdot 10^{270}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.631110063090909634837685639348743915595 \cdot 10^{-306}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r91909 = x;
        double r91910 = y;
        double r91911 = z;
        double r91912 = r91910 / r91911;
        double r91913 = t;
        double r91914 = r91912 * r91913;
        double r91915 = r91914 / r91913;
        double r91916 = r91909 * r91915;
        return r91916;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r91917 = y;
        double r91918 = z;
        double r91919 = r91917 / r91918;
        double r91920 = -4.636236528901048e+270;
        bool r91921 = r91919 <= r91920;
        double r91922 = x;
        double r91923 = r91922 / r91918;
        double r91924 = r91917 * r91923;
        double r91925 = -1.6311100630909096e-306;
        bool r91926 = r91919 <= r91925;
        double r91927 = r91919 * r91922;
        double r91928 = cbrt(r91917);
        double r91929 = r91928 * r91928;
        double r91930 = cbrt(r91918);
        double r91931 = r91930 * r91930;
        double r91932 = r91929 / r91931;
        double r91933 = r91928 / r91930;
        double r91934 = r91933 * r91922;
        double r91935 = r91932 * r91934;
        double r91936 = r91926 ? r91927 : r91935;
        double r91937 = r91921 ? r91924 : r91936;
        return r91937;
}

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) < -4.636236528901048e+270

    1. Initial program 54.7

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

    2. Simplified46.3

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

    4. Applied div-inv46.3

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

    5. Applied associate-*l*0.4

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

    6. Simplified0.3

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

    if -4.636236528901048e+270 < (/ y z) < -1.6311100630909096e-306

    1. Initial program 10.4

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

    2. Simplified0.2

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

    if -1.6311100630909096e-306 < (/ y z)

    1. Initial program 15.7

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

    2. Simplified7.8

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

    4. Applied add-cube-cbrt8.5

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

    5. Applied add-cube-cbrt8.7

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

    6. Applied times-frac8.7

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

    7. Applied associate-*l*2.0

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.636236528901048215946534163640858695462 \cdot 10^{270}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.631110063090909634837685639348743915595 \cdot 10^{-306}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))