Average Error: 6.5 → 1.2
Time: 6.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -12943396756.221923828125 \lor \neg \left(a \le 4.018884300263023536054951700128720971934 \cdot 10^{-127}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -12943396756.221923828125 \lor \neg \left(a \le 4.018884300263023536054951700128720971934 \cdot 10^{-127}\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 r397891 = x;
        double r397892 = y;
        double r397893 = z;
        double r397894 = t;
        double r397895 = r397893 - r397894;
        double r397896 = r397892 * r397895;
        double r397897 = a;
        double r397898 = r397896 / r397897;
        double r397899 = r397891 + r397898;
        return r397899;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r397900 = a;
        double r397901 = -12943396756.221924;
        bool r397902 = r397900 <= r397901;
        double r397903 = 4.0188843002630235e-127;
        bool r397904 = r397900 <= r397903;
        double r397905 = !r397904;
        bool r397906 = r397902 || r397905;
        double r397907 = x;
        double r397908 = y;
        double r397909 = z;
        double r397910 = t;
        double r397911 = r397909 - r397910;
        double r397912 = r397900 / r397911;
        double r397913 = r397908 / r397912;
        double r397914 = r397907 + r397913;
        double r397915 = r397908 * r397911;
        double r397916 = r397915 / r397900;
        double r397917 = r397907 + r397916;
        double r397918 = r397906 ? r397914 : r397917;
        return r397918;
}

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

Original6.5
Target0.7
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -12943396756.221924 or 4.0188843002630235e-127 < a

    1. Initial program 8.9

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

    3. Applied associate-/l*1.4

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

    if -12943396756.221924 < a < 4.0188843002630235e-127

    1. Initial program 0.8

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -12943396756.221923828125 \lor \neg \left(a \le 4.018884300263023536054951700128720971934 \cdot 10^{-127}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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)))