Average Error: 6.2 → 0.7
Time: 9.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -3.9837151397464283 \cdot 10^{91} \lor \neg \left(y \cdot \left(z - t\right) \le 1.4362507429651844 \cdot 10^{239}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{a} \cdot \left(y \cdot \left(z - t\right)\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -3.9837151397464283 \cdot 10^{91} \lor \neg \left(y \cdot \left(z - t\right) \le 1.4362507429651844 \cdot 10^{239}\right):\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{1}{a} \cdot \left(y \cdot \left(z - t\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r384827 = x;
        double r384828 = y;
        double r384829 = z;
        double r384830 = t;
        double r384831 = r384829 - r384830;
        double r384832 = r384828 * r384831;
        double r384833 = a;
        double r384834 = r384832 / r384833;
        double r384835 = r384827 + r384834;
        return r384835;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r384836 = y;
        double r384837 = z;
        double r384838 = t;
        double r384839 = r384837 - r384838;
        double r384840 = r384836 * r384839;
        double r384841 = -3.983715139746428e+91;
        bool r384842 = r384840 <= r384841;
        double r384843 = 1.4362507429651844e+239;
        bool r384844 = r384840 <= r384843;
        double r384845 = !r384844;
        bool r384846 = r384842 || r384845;
        double r384847 = x;
        double r384848 = a;
        double r384849 = r384836 / r384848;
        double r384850 = r384849 * r384839;
        double r384851 = r384847 + r384850;
        double r384852 = 1.0;
        double r384853 = r384852 / r384848;
        double r384854 = r384853 * r384840;
        double r384855 = r384847 + r384854;
        double r384856 = r384846 ? r384851 : r384855;
        return r384856;
}

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
Target0.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -3.983715139746428e+91 or 1.4362507429651844e+239 < (* y (- z t))

    1. Initial program 22.2

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

    3. Applied associate-/l*2.4

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

    5. Applied associate-/r/1.3

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

    if -3.983715139746428e+91 < (* y (- z t)) < 1.4362507429651844e+239

    1. Initial program 0.4

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

    3. Applied associate-/l*6.6

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

    5. Applied div-inv6.6

      \[\leadsto x + \frac{y}{\color{blue}{a \cdot \frac{1}{z - t}}}\]

    6. Applied *-un-lft-identity6.6

      \[\leadsto x + \frac{\color{blue}{1 \cdot y}}{a \cdot \frac{1}{z - t}}\]

    7. Applied times-frac0.5

      \[\leadsto x + \color{blue}{\frac{1}{a} \cdot \frac{y}{\frac{1}{z - t}}}\]

    8. Simplified0.4

      \[\leadsto x + \frac{1}{a} \cdot \color{blue}{\left(y \cdot \left(z - t\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -3.9837151397464283 \cdot 10^{91} \lor \neg \left(y \cdot \left(z - t\right) \le 1.4362507429651844 \cdot 10^{239}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{a} \cdot \left(y \cdot \left(z - t\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 
(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)))