Average Error: 6.1 → 0.5
Time: 3.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.086588240667298 \cdot 10^{268} \lor \neg \left(y \cdot \left(z - t\right) \le 4.3668041271782376 \cdot 10^{219}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -1.086588240667298 \cdot 10^{268} \lor \neg \left(y \cdot \left(z - t\right) \le 4.3668041271782376 \cdot 10^{219}\right):\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

\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 r314429 = x;
        double r314430 = y;
        double r314431 = z;
        double r314432 = t;
        double r314433 = r314431 - r314432;
        double r314434 = r314430 * r314433;
        double r314435 = a;
        double r314436 = r314434 / r314435;
        double r314437 = r314429 + r314436;
        return r314437;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r314438 = y;
        double r314439 = z;
        double r314440 = t;
        double r314441 = r314439 - r314440;
        double r314442 = r314438 * r314441;
        double r314443 = -1.0865882406672983e+268;
        bool r314444 = r314442 <= r314443;
        double r314445 = 4.3668041271782376e+219;
        bool r314446 = r314442 <= r314445;
        double r314447 = !r314446;
        bool r314448 = r314444 || r314447;
        double r314449 = x;
        double r314450 = a;
        double r314451 = r314438 / r314450;
        double r314452 = r314451 * r314441;
        double r314453 = r314449 + r314452;
        double r314454 = r314442 / r314450;
        double r314455 = r314449 + r314454;
        double r314456 = r314448 ? r314453 : r314455;
        return r314456;
}

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

Original6.1
Target0.7
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -1.0865882406672983e+268 or 4.3668041271782376e+219 < (* y (- z t))

    1. Initial program 38.7

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

    3. Applied associate-/l*0.4

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

    5. Applied associate-/r/0.3

      \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)}\]

    if -1.0865882406672983e+268 < (* y (- z t)) < 4.3668041271782376e+219

    1. Initial program 0.5

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.086588240667298 \cdot 10^{268} \lor \neg \left(y \cdot \left(z - t\right) \le 4.3668041271782376 \cdot 10^{219}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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)))