Average Error: 6.1 → 0.5
Time: 18.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 6.770197444411709092251376161345363321712 \cdot 10^{154}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 6.770197444411709092251376161345363321712 \cdot 10^{154}\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 r178244 = x;
        double r178245 = y;
        double r178246 = z;
        double r178247 = t;
        double r178248 = r178246 - r178247;
        double r178249 = r178245 * r178248;
        double r178250 = a;
        double r178251 = r178249 / r178250;
        double r178252 = r178244 + r178251;
        return r178252;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r178253 = y;
        double r178254 = z;
        double r178255 = t;
        double r178256 = r178254 - r178255;
        double r178257 = r178253 * r178256;
        double r178258 = -inf.0;
        bool r178259 = r178257 <= r178258;
        double r178260 = 6.770197444411709e+154;
        bool r178261 = r178257 <= r178260;
        double r178262 = !r178261;
        bool r178263 = r178259 || r178262;
        double r178264 = x;
        double r178265 = a;
        double r178266 = r178265 / r178256;
        double r178267 = r178253 / r178266;
        double r178268 = r178264 + r178267;
        double r178269 = r178257 / r178265;
        double r178270 = r178264 + r178269;
        double r178271 = r178263 ? r178268 : r178270;
        return r178271;
}

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
Target0.6
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)) < -inf.0 or 6.770197444411709e+154 < (* y (- z t))

    1. Initial program 32.4

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

    3. Applied associate-/l*1.4

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

    if -inf.0 < (* y (- z t)) < 6.770197444411709e+154

    1. Initial program 0.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 6.770197444411709092251376161345363321712 \cdot 10^{154}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(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)))