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 r313207 = x;
        double r313208 = y;
        double r313209 = z;
        double r313210 = t;
        double r313211 = r313209 - r313210;
        double r313212 = r313208 * r313211;
        double r313213 = a;
        double r313214 = r313212 / r313213;
        double r313215 = r313207 - r313214;
        return r313215;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r313216 = y;
        double r313217 = z;
        double r313218 = t;
        double r313219 = r313217 - r313218;
        double r313220 = r313216 * r313219;
        double r313221 = -4.06649804702602e+223;
        bool r313222 = r313220 <= r313221;
        double r313223 = 1.8271718225135953e+190;
        bool r313224 = r313220 <= r313223;
        double r313225 = !r313224;
        bool r313226 = r313222 || r313225;
        double r313227 = x;
        double r313228 = a;
        double r313229 = r313228 / r313219;
        double r313230 = r313216 / r313229;
        double r313231 = r313227 - r313230;
        double r313232 = r313220 / r313228;
        double r313233 = r313227 - r313232;
        double r313234 = r313226 ? r313231 : r313233;
        return r313234;
}

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, 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)))