Average Error: 5.9 → 0.6
Time: 3.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.6326385093152292 \cdot 10^{284} \lor \neg \left(y \cdot \left(z - t\right) \le 7.14285184082454088 \cdot 10^{130}\right):\\ \;\;\;\;x + \left(z \cdot \frac{y}{a} + \frac{y}{a} \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -1.6326385093152292 \cdot 10^{284} \lor \neg \left(y \cdot \left(z - t\right) \le 7.14285184082454088 \cdot 10^{130}\right):\\
\;\;\;\;x + \left(z \cdot \frac{y}{a} + \frac{y}{a} \cdot \left(-t\right)\right)\\

\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 r399249 = x;
        double r399250 = y;
        double r399251 = z;
        double r399252 = t;
        double r399253 = r399251 - r399252;
        double r399254 = r399250 * r399253;
        double r399255 = a;
        double r399256 = r399254 / r399255;
        double r399257 = r399249 + r399256;
        return r399257;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r399258 = y;
        double r399259 = z;
        double r399260 = t;
        double r399261 = r399259 - r399260;
        double r399262 = r399258 * r399261;
        double r399263 = -1.6326385093152292e+284;
        bool r399264 = r399262 <= r399263;
        double r399265 = 7.142851840824541e+130;
        bool r399266 = r399262 <= r399265;
        double r399267 = !r399266;
        bool r399268 = r399264 || r399267;
        double r399269 = x;
        double r399270 = a;
        double r399271 = r399258 / r399270;
        double r399272 = r399259 * r399271;
        double r399273 = -r399260;
        double r399274 = r399271 * r399273;
        double r399275 = r399272 + r399274;
        double r399276 = r399269 + r399275;
        double r399277 = r399262 / r399270;
        double r399278 = r399269 + r399277;
        double r399279 = r399268 ? r399276 : r399278;
        return r399279;
}

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

Original5.9
Target0.8
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -1.6326385093152292e+284 or 7.142851840824541e+130 < (* y (- z t))

    1. Initial program 27.6

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

    3. Applied associate-/l*1.9

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

    5. Applied associate-/r/1.3

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

    7. Applied sub-neg1.3

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

    8. Applied distribute-lft-in1.3

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

    9. Simplified1.3

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

    if -1.6326385093152292e+284 < (* y (- z t)) < 7.142851840824541e+130

    1. Initial program 0.4

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.6326385093152292 \cdot 10^{284} \lor \neg \left(y \cdot \left(z - t\right) \le 7.14285184082454088 \cdot 10^{130}\right):\\ \;\;\;\;x + \left(z \cdot \frac{y}{a} + \frac{y}{a} \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(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)))