Average Error: 14.6 → 1.4
Time: 15.3s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.132598746854114829512768870270445047675 \cdot 10^{144}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -9.566229803325124100269745305371770265409 \cdot 10^{-252}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 6.302366347983369041436870740623293996999 \cdot 10^{-316}:\\ \;\;\;\;\left(\sqrt[3]{x} \cdot \left(y \cdot \sqrt[3]{x}\right)\right) \cdot \frac{\sqrt[3]{x}}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.885617898338493029317290072257967706665 \cdot 10^{255}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{x} \cdot \left(y \cdot \sqrt[3]{x}\right)\right) \cdot \frac{\sqrt[3]{x}}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.132598746854114829512768870270445047675 \cdot 10^{144}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -9.566229803325124100269745305371770265409 \cdot 10^{-252}:\\
\;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\

\mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 6.302366347983369041436870740623293996999 \cdot 10^{-316}:\\
\;\;\;\;\left(\sqrt[3]{x} \cdot \left(y \cdot \sqrt[3]{x}\right)\right) \cdot \frac{\sqrt[3]{x}}{z}\\

\mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.885617898338493029317290072257967706665 \cdot 10^{255}:\\
\;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r33683872 = x;
        double r33683873 = y;
        double r33683874 = z;
        double r33683875 = r33683873 / r33683874;
        double r33683876 = t;
        double r33683877 = r33683875 * r33683876;
        double r33683878 = r33683877 / r33683876;
        double r33683879 = r33683872 * r33683878;
        return r33683879;
}
↓
double f(double x, double y, double z, double t) {
        double r33683880 = y;
        double r33683881 = z;
        double r33683882 = r33683880 / r33683881;
        double r33683883 = t;
        double r33683884 = r33683882 * r33683883;
        double r33683885 = r33683884 / r33683883;
        double r33683886 = -1.1325987468541148e+144;
        bool r33683887 = r33683885 <= r33683886;
        double r33683888 = x;
        double r33683889 = r33683888 / r33683881;
        double r33683890 = r33683889 * r33683880;
        double r33683891 = -9.566229803325124e-252;
        bool r33683892 = r33683885 <= r33683891;
        double r33683893 = r33683888 * r33683885;
        double r33683894 = 6.3023663479834e-316;
        bool r33683895 = r33683885 <= r33683894;
        double r33683896 = cbrt(r33683888);
        double r33683897 = r33683880 * r33683896;
        double r33683898 = r33683896 * r33683897;
        double r33683899 = r33683896 / r33683881;
        double r33683900 = r33683898 * r33683899;
        double r33683901 = 1.885617898338493e+255;
        bool r33683902 = r33683885 <= r33683901;
        double r33683903 = r33683902 ? r33683893 : r33683900;
        double r33683904 = r33683895 ? r33683900 : r33683903;
        double r33683905 = r33683892 ? r33683893 : r33683904;
        double r33683906 = r33683887 ? r33683890 : r33683905;
        return r33683906;
}

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

Target

Original14.6
Target1.5
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (/ y z) t) t) < -1.1325987468541148e+144

    1. Initial program 37.5

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

    2. Simplified4.4

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

    if -1.1325987468541148e+144 < (/ (* (/ y z) t) t) < -9.566229803325124e-252 or 6.3023663479834e-316 < (/ (* (/ y z) t) t) < 1.885617898338493e+255

    1. Initial program 0.7

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

    if -9.566229803325124e-252 < (/ (* (/ y z) t) t) < 6.3023663479834e-316 or 1.885617898338493e+255 < (/ (* (/ y z) t) t)

    1. Initial program 32.8

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

    2. Simplified1.6

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

    4. Applied *-un-lft-identity1.6

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

    5. Applied add-cube-cbrt2.2

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

    6. Applied times-frac2.2

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

    7. Applied associate-*r*1.8

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

    8. Simplified1.8

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.132598746854114829512768870270445047675 \cdot 10^{144}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -9.566229803325124100269745305371770265409 \cdot 10^{-252}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 6.302366347983369041436870740623293996999 \cdot 10^{-316}:\\ \;\;\;\;\left(\sqrt[3]{x} \cdot \left(y \cdot \sqrt[3]{x}\right)\right) \cdot \frac{\sqrt[3]{x}}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.885617898338493029317290072257967706665 \cdot 10^{255}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{x} \cdot \left(y \cdot \sqrt[3]{x}\right)\right) \cdot \frac{\sqrt[3]{x}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))