Average Error: 6.2 → 0.8
Time: 10.9s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.57164337169283755 \cdot 10^{297}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.57164337169283755 \cdot 10^{297}:\\
\;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r405890 = x;
        double r405891 = y;
        double r405892 = z;
        double r405893 = r405892 - r405890;
        double r405894 = r405891 * r405893;
        double r405895 = t;
        double r405896 = r405894 / r405895;
        double r405897 = r405890 + r405896;
        return r405897;
}
↓
double f(double x, double y, double z, double t) {
        double r405898 = x;
        double r405899 = y;
        double r405900 = z;
        double r405901 = r405900 - r405898;
        double r405902 = r405899 * r405901;
        double r405903 = t;
        double r405904 = r405902 / r405903;
        double r405905 = r405898 + r405904;
        double r405906 = -3.5716433716928375e+297;
        bool r405907 = r405905 <= r405906;
        double r405908 = r405903 / r405899;
        double r405909 = r405901 / r405908;
        double r405910 = r405898 + r405909;
        double r405911 = 1.8301494225514242e+297;
        bool r405912 = r405905 <= r405911;
        double r405913 = r405903 / r405901;
        double r405914 = r405899 / r405913;
        double r405915 = r405898 + r405914;
        double r405916 = r405912 ? r405905 : r405915;
        double r405917 = r405907 ? r405910 : r405916;
        return r405917;
}

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

Original6.2
Target2.0
Herbie0.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -3.5716433716928375e+297

    1. Initial program 51.7

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

    2. Taylor expanded around 0 51.7

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

    3. Simplified1.4

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

    if -3.5716433716928375e+297 < (+ x (/ (* y (- z x)) t)) < 1.8301494225514242e+297

    1. Initial program 0.6

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

    if 1.8301494225514242e+297 < (+ x (/ (* y (- z x)) t))

    1. Initial program 53.1

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

    3. Applied associate-/l*3.0

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.57164337169283755 \cdot 10^{297}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))