Average Error: 6.5 → 2.1
Time: 3.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.046404802305749277589115866530867327017 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \mathbf{elif}\;x \le 2.249132071309161299573562256453440442682 \cdot 10^{-171}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.046404802305749277589115866530867327017 \cdot 10^{-290}:\\
\;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\

\mathbf{elif}\;x \le 2.249132071309161299573562256453440442682 \cdot 10^{-171}:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r326846 = x;
        double r326847 = y;
        double r326848 = z;
        double r326849 = r326848 - r326846;
        double r326850 = r326847 * r326849;
        double r326851 = t;
        double r326852 = r326850 / r326851;
        double r326853 = r326846 + r326852;
        return r326853;
}
↓
double f(double x, double y, double z, double t) {
        double r326854 = x;
        double r326855 = -1.0464048023057493e-290;
        bool r326856 = r326854 <= r326855;
        double r326857 = y;
        double r326858 = t;
        double r326859 = r326857 / r326858;
        double r326860 = 1.0;
        double r326861 = z;
        double r326862 = r326861 - r326854;
        double r326863 = r326860 / r326862;
        double r326864 = r326859 / r326863;
        double r326865 = r326854 + r326864;
        double r326866 = 2.2491320713091613e-171;
        bool r326867 = r326854 <= r326866;
        double r326868 = r326858 / r326862;
        double r326869 = r326857 / r326868;
        double r326870 = r326854 + r326869;
        double r326871 = r326858 / r326857;
        double r326872 = r326871 / r326862;
        double r326873 = r326860 / r326872;
        double r326874 = r326854 + r326873;
        double r326875 = r326867 ? r326870 : r326874;
        double r326876 = r326856 ? r326865 : r326875;
        return r326876;
}

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

Original6.5
Target2.2
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.0464048023057493e-290

    1. Initial program 6.4

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

    3. Applied clear-num6.5

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

    5. Applied associate-/r*2.0

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z - x}}}\]
    6. Using strategy rm

    7. Applied div-inv2.0

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

    8. Applied associate-/r*2.1

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

    9. Simplified2.0

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

    if -1.0464048023057493e-290 < x < 2.2491320713091613e-171

    1. Initial program 5.5

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

    3. Applied associate-/l*5.0

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

    if 2.2491320713091613e-171 < x

    1. Initial program 6.9

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

    3. Applied clear-num6.9

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

    5. Applied associate-/r*1.1

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z - x}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.046404802305749277589115866530867327017 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \mathbf{elif}\;x \le 2.249132071309161299573562256453440442682 \cdot 10^{-171}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019356 
(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)))