Average Error: 6.1 → 0.5
Time: 19.4s
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 r275760 = x;
        double r275761 = y;
        double r275762 = z;
        double r275763 = t;
        double r275764 = r275762 - r275763;
        double r275765 = r275761 * r275764;
        double r275766 = a;
        double r275767 = r275765 / r275766;
        double r275768 = r275760 + r275767;
        return r275768;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r275769 = y;
        double r275770 = z;
        double r275771 = t;
        double r275772 = r275770 - r275771;
        double r275773 = r275769 * r275772;
        double r275774 = -inf.0;
        bool r275775 = r275773 <= r275774;
        double r275776 = 6.770197444411709e+154;
        bool r275777 = r275773 <= r275776;
        double r275778 = !r275777;
        bool r275779 = r275775 || r275778;
        double r275780 = x;
        double r275781 = a;
        double r275782 = r275781 / r275772;
        double r275783 = r275769 / r275782;
        double r275784 = r275780 + r275783;
        double r275785 = r275773 / r275781;
        double r275786 = r275780 + r275785;
        double r275787 = r275779 ? r275784 : r275786;
        return r275787;
}

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)))