Average Error: 6.3 → 1.3
Time: 5.5s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -6.13167225046898742 \cdot 10^{67}:\\ \;\;\;\;x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{y} \cdot \frac{z - x}{\sqrt[3]{t}}}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 5.76803007472270124 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -6.13167225046898742 \cdot 10^{67}:\\
\;\;\;\;x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{y} \cdot \frac{z - x}{\sqrt[3]{t}}}{\sqrt[3]{t}}\\

\mathbf{elif}\;t \le 5.76803007472270124 \cdot 10^{-36}:\\
\;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r409889 = x;
        double r409890 = y;
        double r409891 = z;
        double r409892 = r409891 - r409889;
        double r409893 = r409890 * r409892;
        double r409894 = t;
        double r409895 = r409893 / r409894;
        double r409896 = r409889 + r409895;
        return r409896;
}
↓
double f(double x, double y, double z, double t) {
        double r409897 = t;
        double r409898 = -6.131672250468987e+67;
        bool r409899 = r409897 <= r409898;
        double r409900 = x;
        double r409901 = y;
        double r409902 = cbrt(r409901);
        double r409903 = r409902 * r409902;
        double r409904 = cbrt(r409897);
        double r409905 = r409903 / r409904;
        double r409906 = z;
        double r409907 = r409906 - r409900;
        double r409908 = r409907 / r409904;
        double r409909 = r409902 * r409908;
        double r409910 = r409909 / r409904;
        double r409911 = r409905 * r409910;
        double r409912 = r409900 + r409911;
        double r409913 = 5.768030074722701e-36;
        bool r409914 = r409897 <= r409913;
        double r409915 = 1.0;
        double r409916 = r409901 * r409907;
        double r409917 = r409897 / r409916;
        double r409918 = r409915 / r409917;
        double r409919 = r409900 + r409918;
        double r409920 = r409907 / r409897;
        double r409921 = r409901 * r409920;
        double r409922 = r409900 + r409921;
        double r409923 = r409914 ? r409919 : r409922;
        double r409924 = r409899 ? r409912 : r409923;
        return r409924;
}

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

Original6.3
Target1.9
Herbie1.3
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if t < -6.131672250468987e+67

    1. Initial program 11.5

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt11.8

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

    4. Applied times-frac1.0

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt1.1

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

    7. Applied times-frac1.1

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

    8. Applied associate-*l*0.6

      \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\right)}\]
    9. Using strategy rm

    10. Applied associate-*r/0.6

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

    11. Simplified0.6

      \[\leadsto x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt[3]{y} \cdot \frac{z - x}{\sqrt[3]{t}}}}{\sqrt[3]{t}}\]

    if -6.131672250468987e+67 < t < 5.768030074722701e-36

    1. Initial program 1.8

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
    2. Using strategy rm

    3. Applied clear-num1.9

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

    if 5.768030074722701e-36 < t

    1. Initial program 8.1

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity8.1

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

    4. Applied times-frac1.2

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

    5. Simplified1.2

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -6.13167225046898742 \cdot 10^{67}:\\ \;\;\;\;x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{y} \cdot \frac{z - x}{\sqrt[3]{t}}}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 5.76803007472270124 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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