Average Error: 6.8 → 1.9
Time: 4.1s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.0778965796828648 \cdot 10^{-103} \lor \neg \left(x \le 9.10716533387276044 \cdot 10^{-93}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \left(\frac{\sqrt[3]{y}}{t} \cdot \left(z - x\right)\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.0778965796828648 \cdot 10^{-103} \lor \neg \left(x \le 9.10716533387276044 \cdot 10^{-93}\right):\\
\;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \left(\frac{\sqrt[3]{y}}{t} \cdot \left(z - x\right)\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r337975 = x;
        double r337976 = y;
        double r337977 = z;
        double r337978 = r337977 - r337975;
        double r337979 = r337976 * r337978;
        double r337980 = t;
        double r337981 = r337979 / r337980;
        double r337982 = r337975 + r337981;
        return r337982;
}
↓
double f(double x, double y, double z, double t) {
        double r337983 = x;
        double r337984 = -2.0778965796828648e-103;
        bool r337985 = r337983 <= r337984;
        double r337986 = 9.10716533387276e-93;
        bool r337987 = r337983 <= r337986;
        double r337988 = !r337987;
        bool r337989 = r337985 || r337988;
        double r337990 = y;
        double r337991 = t;
        double r337992 = r337990 / r337991;
        double r337993 = z;
        double r337994 = r337993 - r337983;
        double r337995 = r337992 * r337994;
        double r337996 = r337983 + r337995;
        double r337997 = cbrt(r337990);
        double r337998 = r337997 * r337997;
        double r337999 = 1.0;
        double r338000 = r337998 / r337999;
        double r338001 = r337997 / r337991;
        double r338002 = r338001 * r337994;
        double r338003 = r338000 * r338002;
        double r338004 = r337983 + r338003;
        double r338005 = r337989 ? r337996 : r338004;
        return r338005;
}

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

Original6.8
Target2.1
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if x < -2.0778965796828648e-103 or 9.10716533387276e-93 < x

    1. Initial program 7.9

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

    3. Applied associate-/l*6.7

      \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z - x}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.5

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

    if -2.0778965796828648e-103 < x < 9.10716533387276e-93

    1. Initial program 5.0

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

    3. Applied associate-/l*5.0

      \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z - x}}}\]
    4. Using strategy rm

    5. Applied associate-/r/4.8

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

    7. Applied *-un-lft-identity4.8

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

    8. Applied add-cube-cbrt5.5

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

    9. Applied times-frac5.5

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

    10. Applied associate-*l*4.3

      \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \left(\frac{\sqrt[3]{y}}{t} \cdot \left(z - x\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.0778965796828648 \cdot 10^{-103} \lor \neg \left(x \le 9.10716533387276044 \cdot 10^{-93}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \left(\frac{\sqrt[3]{y}}{t} \cdot \left(z - x\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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)))