Average Error: 15.1 → 1.3
Time: 27.8s
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 r55008 = x;
        double r55009 = y;
        double r55010 = z;
        double r55011 = r55009 / r55010;
        double r55012 = t;
        double r55013 = r55011 * r55012;
        double r55014 = r55013 / r55012;
        double r55015 = r55008 * r55014;
        return r55015;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r55016 = y;
        double r55017 = z;
        double r55018 = r55016 / r55017;
        double r55019 = -4.636236528901048e+270;
        bool r55020 = r55018 <= r55019;
        double r55021 = x;
        double r55022 = r55021 / r55017;
        double r55023 = r55016 * r55022;
        double r55024 = -1.6311100630909096e-306;
        bool r55025 = r55018 <= r55024;
        double r55026 = r55018 * r55021;
        double r55027 = cbrt(r55016);
        double r55028 = r55027 * r55027;
        double r55029 = cbrt(r55017);
        double r55030 = r55029 * r55029;
        double r55031 = r55028 / r55030;
        double r55032 = r55027 / r55029;
        double r55033 = r55032 * r55021;
        double r55034 = r55031 * r55033;
        double r55035 = r55025 ? r55026 : r55034;
        double r55036 = r55020 ? r55023 : r55035;
        return r55036;
}

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 +o rules:numerics
(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)))