Average Error: 6.0 → 1.6
Time: 5.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2486.642887294508 \lor \neg \left(y \le 7.8098547636132432 \cdot 10^{-193}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2486.642887294508 \lor \neg \left(y \le 7.8098547636132432 \cdot 10^{-193}\right):\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r263720 = x;
        double r263721 = y;
        double r263722 = z;
        double r263723 = t;
        double r263724 = r263722 - r263723;
        double r263725 = r263721 * r263724;
        double r263726 = a;
        double r263727 = r263725 / r263726;
        double r263728 = r263720 + r263727;
        return r263728;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r263729 = y;
        double r263730 = -2486.642887294508;
        bool r263731 = r263729 <= r263730;
        double r263732 = 7.809854763613243e-193;
        bool r263733 = r263729 <= r263732;
        double r263734 = !r263733;
        bool r263735 = r263731 || r263734;
        double r263736 = x;
        double r263737 = a;
        double r263738 = z;
        double r263739 = t;
        double r263740 = r263738 - r263739;
        double r263741 = r263737 / r263740;
        double r263742 = r263729 / r263741;
        double r263743 = r263736 + r263742;
        double r263744 = r263729 * r263740;
        double r263745 = r263744 / r263737;
        double r263746 = r263736 + r263745;
        double r263747 = r263735 ? r263743 : r263746;
        return r263747;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.0
Target0.6
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2486.642887294508 or 7.809854763613243e-193 < y

    1. Initial program 10.3

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

    3. Applied associate-/l*2.4

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

    if -2486.642887294508 < y < 7.809854763613243e-193

    1. Initial program 0.5

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2486.642887294508 \lor \neg \left(y \le 7.8098547636132432 \cdot 10^{-193}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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