Average Error: 6.0 → 1.6
Time: 5.8s
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 r355685 = x;
        double r355686 = y;
        double r355687 = z;
        double r355688 = t;
        double r355689 = r355687 - r355688;
        double r355690 = r355686 * r355689;
        double r355691 = a;
        double r355692 = r355690 / r355691;
        double r355693 = r355685 - r355692;
        return r355693;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r355694 = y;
        double r355695 = -2486.642887294508;
        bool r355696 = r355694 <= r355695;
        double r355697 = 7.809854763613243e-193;
        bool r355698 = r355694 <= r355697;
        double r355699 = !r355698;
        bool r355700 = r355696 || r355699;
        double r355701 = x;
        double r355702 = a;
        double r355703 = z;
        double r355704 = t;
        double r355705 = r355703 - r355704;
        double r355706 = r355702 / r355705;
        double r355707 = r355694 / r355706;
        double r355708 = r355701 - r355707;
        double r355709 = r355694 * r355705;
        double r355710 = r355709 / r355702;
        double r355711 = r355701 - r355710;
        double r355712 = r355700 ? r355708 : r355711;
        return r355712;
}

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, F"
  :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)))