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 r261297 = x;
        double r261298 = y;
        double r261299 = z;
        double r261300 = t;
        double r261301 = r261299 - r261300;
        double r261302 = r261298 * r261301;
        double r261303 = a;
        double r261304 = r261302 / r261303;
        double r261305 = r261297 - r261304;
        return r261305;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r261306 = y;
        double r261307 = -2486.642887294508;
        bool r261308 = r261306 <= r261307;
        double r261309 = 7.809854763613243e-193;
        bool r261310 = r261306 <= r261309;
        double r261311 = !r261310;
        bool r261312 = r261308 || r261311;
        double r261313 = x;
        double r261314 = a;
        double r261315 = z;
        double r261316 = t;
        double r261317 = r261315 - r261316;
        double r261318 = r261314 / r261317;
        double r261319 = r261306 / r261318;
        double r261320 = r261313 - r261319;
        double r261321 = r261306 * r261317;
        double r261322 = r261321 / r261314;
        double r261323 = r261313 - r261322;
        double r261324 = r261312 ? r261320 : r261323;
        return r261324;
}

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)))