Average Error: 6.2 → 0.5
Time: 4.4s
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 r393120 = x;
        double r393121 = y;
        double r393122 = z;
        double r393123 = t;
        double r393124 = r393122 - r393123;
        double r393125 = r393121 * r393124;
        double r393126 = a;
        double r393127 = r393125 / r393126;
        double r393128 = r393120 - r393127;
        return r393128;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r393129 = y;
        double r393130 = z;
        double r393131 = t;
        double r393132 = r393130 - r393131;
        double r393133 = r393129 * r393132;
        double r393134 = -4.06649804702602e+223;
        bool r393135 = r393133 <= r393134;
        double r393136 = 1.8271718225135953e+190;
        bool r393137 = r393133 <= r393136;
        double r393138 = !r393137;
        bool r393139 = r393135 || r393138;
        double r393140 = x;
        double r393141 = a;
        double r393142 = r393141 / r393132;
        double r393143 = r393129 / r393142;
        double r393144 = r393140 - r393143;
        double r393145 = r393133 / r393141;
        double r393146 = r393140 - r393145;
        double r393147 = r393139 ? r393144 : r393146;
        return r393147;
}

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)))