Average Error: 6.2 → 0.5
Time: 4.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -4.066498047026020222506690802038445332874 \cdot 10^{223} \lor \neg \left(y \cdot \left(z - t\right) \le 1.827171822513595294503001801235013170875 \cdot 10^{190}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -4.066498047026020222506690802038445332874 \cdot 10^{223} \lor \neg \left(y \cdot \left(z - t\right) \le 1.827171822513595294503001801235013170875 \cdot 10^{190}\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 r363366 = x;
        double r363367 = y;
        double r363368 = z;
        double r363369 = t;
        double r363370 = r363368 - r363369;
        double r363371 = r363367 * r363370;
        double r363372 = a;
        double r363373 = r363371 / r363372;
        double r363374 = r363366 + r363373;
        return r363374;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r363375 = y;
        double r363376 = z;
        double r363377 = t;
        double r363378 = r363376 - r363377;
        double r363379 = r363375 * r363378;
        double r363380 = -4.06649804702602e+223;
        bool r363381 = r363379 <= r363380;
        double r363382 = 1.8271718225135953e+190;
        bool r363383 = r363379 <= r363382;
        double r363384 = !r363383;
        bool r363385 = r363381 || r363384;
        double r363386 = x;
        double r363387 = a;
        double r363388 = r363387 / r363378;
        double r363389 = r363375 / r363388;
        double r363390 = r363386 + r363389;
        double r363391 = r363379 / r363387;
        double r363392 = r363386 + r363391;
        double r363393 = r363385 ? r363390 : r363392;
        return r363393;
}

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

Original6.2
Target0.7
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -4.06649804702602e+223 or 1.8271718225135953e+190 < (* y (- z t))

    1. Initial program 29.9

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

    3. Applied associate-/l*0.7

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

    if -4.06649804702602e+223 < (* y (- z t)) < 1.8271718225135953e+190

    1. Initial program 0.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -4.066498047026020222506690802038445332874 \cdot 10^{223} \lor \neg \left(y \cdot \left(z - t\right) \le 1.827171822513595294503001801235013170875 \cdot 10^{190}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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)))